Solve Ratio and Rate Word Problems

Students solve multistep ratio and rate problems set in real-world contexts such as speed, density, recipe scaling, and currency exchange. They identify the relevant ratio, set up a proportion or equation, and interpret the result.

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Real questions from this skill, graded here. No account, and nothing is saved.

Grade 7 · Ratios and Proportional Relationships · question 1 of 3

0 of 20

20 rungs. A star at the top.

7 : = 14 : 10

How it is taught

0:00 of 4:00

A unit price is total cost divided by the number of ounces.

Keep the units matched: dollars per ounce.

Read it: Ratio and rate problems

2 laps in 5 minutes. A table keeps that pace in every column: 4 to 10, 6 to 15, 8 to 20. Each column is 2 : 5 times one number.

Find the number the known term was multiplied or divided by.
Do the same to the other term.
Check: the new pair is the old ratio times one number.

Equal ratios scale both terms by the same number, so the pace stays the same.

8 laps in 20 minutes is the same pace as 2 laps in 5 minutes: both are 2 : 5 times 4.

Adding the same number to both breaks the ratio: 2 + 6 = 8, but 5 + 6 = 11, and 8 : 11 is a different pace.

Multiply or divide both terms by the same number.

Adding 6 to both terms: 8 : 11.

Scale both by 4: 2 × 4 = 8 and 5 × 4 = 20, so 8 : 20.

13 : 18 = 39 : ___ — 54. 39 is 13 × 3, so the other term is 18 × 3 = 54.

A car drives 120 miles in 2 hours — how far in 5 hours?

A car drives one hundred twenty miles in two hours. At the same speed, how far will it go in five hours?

Let's organize what we know in a ratio table — miles on top, hours on the bottom.

We know one hundred twenty miles in two hours.

And we want to find the miles for five hours.

First, let's find the unit rate — how many miles in just one hour.

Divide miles by hours: one hundred twenty divided by two.

That's sixty miles per hour. This is our unit rate.

Now use the unit rate to scale up. Sixty miles each hour, for five hours.

Grade 7 · Using a unit rate to scale a real-world ratio

Multiply: sixty times five.

Three hundred miles.

At the same rate, the car travels three hundred miles in five hours. Great work!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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Standard

CCSS.7.RP.A.3

Use proportional relationships to solve multistep ratio and percent problems (simple interest, tax, markups/markdowns, gratuities, commissions, fees, percent increase/decrease, percent error)

Grade 7

Quoted from the Common Core State Standards.

Where this sits

Comes after

Leads to

Solve Problems Involving Scale Drawings

What a star here means

A star here is the top of a twenty-rung ladder, in four blocks of equal length — three of facts and one of the skill used in a real question — where a right answer climbs one rung and a wrong one drops back to the start of the block, never below it. The star is kept for good. How we grade

All of Grade 7

This is one rung of 40 in Grade 7 mathematics, in the order they build on each other.

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