Chapter 7 — worked answers and marking guidance
All chapter review and practice examination items
Chapter review solutions
Calculate 1/2 + 3/4. Simplify.
Use the common denominator 4, then add the equal-size parts. The simplified result is 1 1/4.
Calculate 2/3 + 2/3. Simplify.
Use the common denominator 3, then add the equal-size parts. The simplified result is 1 1/3.
Calculate 2 1/4 + 1/2.
Add the fractional parts with a common denominator. Include the original 2 wholes; regroup if their sum reaches a whole.
Calculate 1 5/8 + 3 1/2.
Combine wholes (1+3) and fractional parts (5/8+1/2); rename any extra whole.
Calculate 4 3/4 − 1/4.
Rename one whole as denominator-sized parts if needed. The remaining quantity is 4 1/2.
Calculate 4 1/2 − 2 1/2.
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 4/5 + 4/5. Simplify.
Use the common denominator 5, then add the equal-size parts. The simplified result is 1 3/5.
Calculate 2/3 + 1/3. Simplify.
Use the common denominator 3, then add the equal-size parts. The simplified result is 1.
Calculate 4 2/3 + 2/3.
Add the fractional parts with a common denominator. Include the original 4 wholes; regroup if their sum reaches a whole.
Calculate 2 1/2 + 1 1/3.
Combine wholes (2+1) and fractional parts (1/2+1/3); rename any extra whole.
Calculate 4 1/2 − 1/2.
Rename one whole as denominator-sized parts if needed. The remaining quantity is 4.
Calculate 2 1/4 − 1 1/2.
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 7/10 + 9/10. Simplify.
Use the common denominator 10, then add the equal-size parts. The simplified result is 1 3/5.
Calculate 3/5 + 3/5. Simplify.
Use the common denominator 5, then add the equal-size parts. The simplified result is 1 1/5.
Calculate 5 7/12 + 1/3.
Add the fractional parts with a common denominator. Include the original 5 wholes; regroup if their sum reaches a whole.
Calculate 3 3/4 + 1 1/3.
Combine wholes (3+1) and fractional parts (3/4+1/3); rename any extra whole.
Calculate 1 1/2 − 1/2.
Rename one whole as denominator-sized parts if needed. The remaining quantity is 1.
Calculate 4 1/12 − 3 1/3.
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 2/3 + 1/6. Simplify.
Use the common denominator 6, then add the equal-size parts. The simplified result is 5/6.
Calculate 3/5 + 2/5. Simplify.
Use the common denominator 5, then add the equal-size parts. The simplified result is 1.
Calculate 5 1/4 + 1/2.
Add the fractional parts with a common denominator. Include the original 5 wholes; regroup if their sum reaches a whole.
Calculate 5 3/5 + 2 4/5.
Combine wholes (5+2) and fractional parts (3/5+4/5); rename any extra whole.
Calculate 3 1/4 − 1/2.
Rename one whole as denominator-sized parts if needed. The remaining quantity is 2 3/4.
Calculate 5 2/3 − 4 5/6.
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Calculate 1/8 + 3/8. Simplify.
Use the common denominator 8, then add the equal-size parts. The simplified result is 1/2.
Calculate 2/3 − 1/3. Simplify.
Use the common denominator 3, then subtract the equal-size parts. The simplified result is 1/3.
Calculate 2 9/10 + 4/5.
Add the fractional parts with a common denominator. Include the original 2 wholes; regroup if their sum reaches a whole.
A student calculates 1/10 + 8/10 and writes 9/20. Identify the mistake and give the correct simplified answer.
Both pieces are 10ths, so combine numerators and keep the denominator. The result is 9/10.
A student calculates 1/3 + 3/4 and writes 4/7. Identify the mistake and give the correct simplified answer.
Use equal-size fractional parts with denominator 12; the correct sum is 1 1/12.
A student calculates 2 1/4 + 1/2 and writes 2 2/6. Identify the mistake and give the correct simplified answer.
Convert 1/2 into 2/4 and combine with 1/4, keeping 2 whole units. The total is 2 3/4.
A student calculates 4 1/2 + 2 2/3 and writes 6 3/5. Identify the mistake and give the correct simplified answer.
Combine 6 wholes and 3/6+4/6=7/6, regrouping one additional whole to reach 7 1/6.
A student calculates 3 1/4 − 3/4 and writes 3 2/4. Identify the mistake and give the correct simplified answer.
Rename one whole as four fourths before subtracting; the correct difference is 2 1/2.
A student calculates 5 1/4 − 1 3/4 and writes 4 2/4. Identify the mistake and give the correct simplified answer.
Exchange one whole for four fourths, then subtract the whole and fractional parts. The difference is 3 1/2.
Practice examination solutions and scoring
A student calculates 3/6 + 2/6 and writes 5/12. Identify the mistake and give the correct simplified answer.
Both pieces are 6ths, so combine numerators and keep the denominator. The result is 5/6.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.
A student calculates 2/5 + 1/2 and writes 3/7. Identify the mistake and give the correct simplified answer.
Use equal-size fractional parts with denominator 10; the correct sum is 9/10.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.
A student calculates 1 1/4 + 1/2 and writes 1 2/6. Identify the mistake and give the correct simplified answer.
Convert 1/2 into 2/4 and combine with 1/4, keeping 1 whole units. The total is 1 3/4.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.
A student calculates 1 1/2 + 2 2/3 and writes 3 3/5. Identify the mistake and give the correct simplified answer.
Combine 3 wholes and 3/6+4/6=7/6, regrouping one additional whole to reach 4 1/6.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.
A student calculates 5 1/4 − 3/4 and writes 5 2/4. Identify the mistake and give the correct simplified answer.
Rename one whole as four fourths before subtracting; the correct difference is 4 1/2.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.
A student calculates 3 1/4 − 1 3/4 and writes 2 2/4. Identify the mistake and give the correct simplified answer.
Exchange one whole for four fourths, then subtract the whole and fractional parts. The difference is 1 1/2.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.
Calculate 1/2 − 1/2. Simplify.
Use the common denominator 2, then subtract the equal-size parts. The simplified result is 0.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 5 5/6 + 2/3.
Add the fractional parts with a common denominator. Include the original 5 wholes; regroup if their sum reaches a whole.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 1 1/4 + 3 1/2.
Combine wholes (1+3) and fractional parts (1/4+1/2); rename any extra whole.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 4 5/8 − 3/4.
Rename one whole as denominator-sized parts if needed. The remaining quantity is 3 7/8.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 5 2/3 − 4 2/3.
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 4/5 + 9/10. Simplify.
Use the common denominator 10, then add the equal-size parts. The simplified result is 1 7/10.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 3 4/5 + 2/5.
Add the fractional parts with a common denominator. Include the original 3 wholes; regroup if their sum reaches a whole.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 5 5/6 + 1 1/6.
Combine wholes (5+1) and fractional parts (5/6+1/6); rename any extra whole.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 2 3/8 − 1/4.
Rename one whole as denominator-sized parts if needed. The remaining quantity is 2 1/8.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 5 1/4 − 4 1/2.
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 5/6 + 5/6. Simplify.
Use the common denominator 6, then add the equal-size parts. The simplified result is 1 2/3.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 5/6 + 1/2. Simplify.
Use the common denominator 6, then add the equal-size parts. The simplified result is 1 1/3.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 3 5/8 + 2 1/2.
Combine wholes (3+2) and fractional parts (5/8+1/2); rename any extra whole.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 5 1/4 − 5/6.
Rename one whole as denominator-sized parts if needed. The remaining quantity is 4 5/12.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 1 1/2 − 1 1/2.
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 5/6 + 1/6. Simplify.
Use the common denominator 6, then add the equal-size parts. The simplified result is 1.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 1/2 + 1/2. Simplify.
Use the common denominator 2, then add the equal-size parts. The simplified result is 1.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 5 3/4 + 1/2.
Add the fractional parts with a common denominator. Include the original 5 wholes; regroup if their sum reaches a whole.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 1 1/10 − 3/5.
Rename one whole as denominator-sized parts if needed. The remaining quantity is 1/2.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 5 5/6 − 5 1/3.
Subtract whole quantities and equivalent fractional parts, borrowing one whole if the first fractional part is smaller.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 7/8 + 3/8. Simplify.
Use the common denominator 8, then add the equal-size parts. The simplified result is 1 1/4.
Scoring (2 points): Award one point for a sound method and one for the correct result.
A student calculates 2/6 + 2/6 and writes 4/12. Identify the mistake and give the correct simplified answer.
Both pieces are 6ths, so combine numerators and keep the denominator. The result is 2/3.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.
A student calculates 1/2 + 1/3 and writes 2/5. Identify the mistake and give the correct simplified answer.
Use equal-size fractional parts with denominator 6; the correct sum is 5/6.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.
A student calculates 4 1/4 + 1/2 and writes 4 2/6. Identify the mistake and give the correct simplified answer.
Convert 1/2 into 2/4 and combine with 1/4, keeping 4 whole units. The total is 4 3/4.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.
A student calculates 3 1/2 + 2 2/3 and writes 5 3/5. Identify the mistake and give the correct simplified answer.
Combine 5 wholes and 3/6+4/6=7/6, regrouping one additional whole to reach 6 1/6.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.
A student calculates 2 1/4 − 3/4 and writes 2 2/4. Identify the mistake and give the correct simplified answer.
Rename one whole as four fourths before subtracting; the correct difference is 1 1/2.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.
A student calculates 4 1/4 − 2 3/4 and writes 2 2/4. Identify the mistake and give the correct simplified answer.
Exchange one whole for four fourths, then subtract the whole and fractional parts. The difference is 1 1/2.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.