L7 · Rational Numbers in the Real World (including Percent Applications)

Learning goal

“I can solve multi-step real-world problems with rational numbers - balances, temperatures, measurements, averages, scaling - and use percent inside money problems (discounts, tips, tax) as an application of rational multiplication.”

Balance — the signed amount in an account: negative means overdrawn (owing the bank), positive means money available.

Discount — an amount taken OFF a price; a 25% discount means paying the other 75% - a rational multiplication of the price.

Tax (on a purchase) — an amount ADDED to the (already discounted) price, computed as a percent of the price actually being paid.

Average (mean) — the sum of values divided by the count of values - addition and division of rationals working together.

Worked example

Maya's account balance is -$36.00. She deposits $60.00, then spends 3/4 of her new balance on climbing gear. What is her balance now? Step 1: Deposit: -36 + 60 = 24. Balance: $24.00. (L2 addition of rationals.) Step 2: She spends 3/4 OF the new balance - "of" is multiplication: 3/4 x 24 = 18. She spends $18.00. (L3/L5 multiplication.) Step 3: Remainder: 24 - 18 = 6. Final balance: $6.00. Say it plainly: nothing new was invented - the problem was unpacked into the operations already mastered, in the order the story tells them. Order of the STORY, checked by the order of operations (L6).

Check yourself — explain it

Why is Step 2 a multiplication and not a division?

Paired problem — example still visible

A balance of -$15.25 receives a $40.00 deposit, then a $12.50 payment leaves the account. Final balance? -> -15.25 + 40 = 24.75; 24.75 - 12.50 = $12.25

Faded completion — last step is yours

"Balance -$8.40; add a $20 deposit: -8.40 + 20 = $11.60. Then pay out half the balance: 1/2 x 11.60 = 5.80, leaving ___." -> $5.80

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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