Grade 7 Complex Fractions and Unit Rates
Complex fractions and unit rates for grade 7 — simplify the stacked fraction, then divide to find the rate. Sixteen problems with a full answer key.
Simplify each complex fraction. For the word problems, divide to find the unit rate.
- 1.(1/2) ÷ (1/4) =
- 2.(3/4) ÷ (1/8) =
- 3.(2/3) ÷ (1/6) =
- 4.(1/2) ÷ (3/4) =
- 5.(5/6) ÷ (2/3) =
- 6.(3/8) ÷ (1/2) =
- 7.(7/10) ÷ (1/5) =
- 8.(2/5) ÷ (4/15) =
- 9.A runner covers 1/2 mile in 1/4 hour. What is the unit rate in miles per hour?
- 10.A snail travels 1/8 foot in 1/2 minute. What is the unit rate in feet per minute?
- 11.A recipe uses 3/4 cup of flour for 1/2 of a batch. What is the unit rate in cups per batch?
- 12.A hose delivers 2/3 gallon in 1/6 minute. What is the unit rate in gallons per minute?
- 13.2/3 of a can of paint covers 1/2 of a wall. What is the unit rate in walls per can?
- 14.A cyclist rides 3 1/2 miles in 1/4 hour. What is the unit rate in miles per hour?
- 15.A machine finishes 5/8 of a part in 1/4 hour. What is the unit rate in parts per hour?
- 16.A pipe leaks 3/10 liter in 3/4 hour. What is the unit rate in liters per hour?
What this worksheet covers
Sixteen fraction problems fill the page, and the complete key sits behind them in the same PDF. Within that, the problems are written as situations, so a student has to translate before they can calculate; several problems use mixed numbers, which have to be handled without dropping the whole-number part. The whole sheet sits inside Common Core 7.RP.1, in the grade 7 Ratios & Proportional Relationships strand.
Skills practiced
Grade 7 sits in the stretch of the fractions progression concerned with negative rational numbers, complex fractions, repeating decimals. Concretely, the page tests whether a student can read a situation and choose an operation before computing and work in fractional units and simplify the result. Consistency across the page matters more than any single answer on it.
How to use this worksheet
Have the student estimate before computing, then compare. At this level an answer that is wildly off should announce itself, and building that reflex matters as much as the sixteen answers themselves. Date the sheet before filing it. A page from six weeks ago is the cheapest evidence you have that something is sticking.
One mistake to watch for
Bigger denominator means bigger fraction: 1/8 is judged larger than 1/3.
Whole-number ordering is being applied to the denominator, where the relationship is inverted.
Cut the same strip into 3 and into 8 pieces side by side. More pieces from one whole means smaller pieces — the denominator counts how many the whole was split into.
Related worksheets
A step either side
Fractions either side of grade 7, for stepping the difficulty rather than repeating it.
- Grade 6 Dividing Fractions — grade 6, 16 problems
- Grade 8 Repeating Decimals as Fractions — grade 8, 16 problems
Free to download, free to print, and free to photocopy for a whole class — this fractions sheet and its key are one PDF, aimed at negative rational numbers, complex fractions, repeating decimals.