Money, Decimals, and Fractions
Semester 4B · Chapter 13 · Lesson 7 · MATH-4B-C13-L07
Before you begin: prerequisite check
Recall: 3B money; 12.05–12.06. Attempt these questions independently first.
Calculate 5.06 − 1.65.
Show answer and reasoning
506 hundredths minus 165 hundredths = 341 hundredths = 3.41.
Calculate 7.42 − 1.71.
Show answer and reasoning
742 hundredths minus 171 hundredths = 571 hundredths = 5.71.
Calculate 6.15 − 2.61.
Show answer and reasoning
615 hundredths minus 261 hundredths = 354 hundredths = 3.54.
Key vocabulary
- decimal point
- separator between whole units and fractional place values
- regroup
- exchange equivalent place-value units
- hundredth
- one hundredth of a whole
- exact amount
- quantity without rounding
Understand the concept
One dollar consists of one hundred cents. A dollar-and-cent amount such as $3.45 is three dollars plus 45 hundredths of a dollar. Adding $2.75 and $1.60 is the same as adding 275 and 160 cents: 435 cents, or $4.35. Treat cents as exact hundredths rather than approximations, and label the answer with dollars or cents. Check that a computed change amount cannot exceed the money given when all prices are positive.
Fully worked examples and immediate checks
Read each example, predict how to begin, then follow its numerical explanation. The check below it is a fresh problem.
Worked example 1
An item costs $1.44 and another costs $2.10. What is their exact combined price?
Add cents exactly: 144+210=354 cents = $3.54.
Check 1: try it yourself
An item costs $6.96 and another costs $1.12. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 696+112=808 cents = $8.08.
Worked example 2
An item costs $5.69 and another costs $1.23. What is their exact combined price?
Add cents exactly: 569+123=692 cents = $6.92.
Check 2: try it yourself
An item costs $4.16 and another costs $1.73. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 416+173=589 cents = $5.89.
Worked example 3
An item costs $5.93 and another costs $3.00. What is their exact combined price?
Add cents exactly: 593+300=893 cents = $8.93.
Check 3: try it yourself
An item costs $3.39 and another costs $1.97. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 339+197=536 cents = $5.36.
Guided practice
An item costs $3.47 and another costs $2.16. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 347+216=563 cents = $5.63.
An item costs $5.12 and another costs $2.10. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 512+210=722 cents = $7.22.
An item costs $3.88 and another costs $3.21. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 388+321=709 cents = $7.09.
An item costs $5.54 and another costs $3.40. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 554+340=894 cents = $8.94.
An item costs $4.46 and another costs $3.39. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 446+339=785 cents = $7.85.
Independent practice
An item costs $3.94 and another costs $1.50. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 394+150=544 cents = $5.44.
An item costs $3.12 and another costs $1.15. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 312+115=427 cents = $4.27.
An item costs $1.33 and another costs $2.81. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 133+281=414 cents = $4.14.
An item costs $4.31 and another costs $2.26. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 431+226=657 cents = $6.57.
An item costs $2.29 and another costs $1.45. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 229+145=374 cents = $3.74.
An item costs $6.96 and another costs $1.19. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 696+119=815 cents = $8.15.
An item costs $2.08 and another costs $3.47. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 208+347=555 cents = $5.55.
An item costs $6.69 and another costs $1.95. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 669+195=864 cents = $8.64.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
An item costs $6.47 and another costs $3.35. What is their exact combined price? Explain how place value or a model can check your result.
Show answer and reasoning
Add cents exactly: 647+335=982 cents = $9.82. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “A shop can round both prices before giving the exact total.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: an exact total must keep cents. For example, $1.49 + $1.49 = $2.98, not $2.00. Explain the relevant quantities or properties, not merely the final answer.
Exit check
An item costs $1.33 and another costs $2.54. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 133+254=387 cents = $3.87.
An item costs $6.95 and another costs $2.08. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 695+208=903 cents = $9.03.
An item costs $2.20 and another costs $2.58. What is their exact combined price?
Show answer and reasoning
Add cents exactly: 220+258=478 cents = $4.78.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.