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.
Download
Three different problem sets — same skill, same layout, fresh numbers.
Preview — Set A
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 fractions problems fill this drill page; problem 6 asks "(3/8) ÷ (1/2)", and the sheet stays at that level throughout. Within that, each problem arrives as a few sentences of context rather than a bare expression and several problems use mixed numbers, which have to be handled without dropping the whole-number part. Further down, problem 11 asks "A recipe uses 3/4 cup of flour for 1/2 of a batch. What is…". Common Core 7.RP.1 is the slot this page fills.
Skills practiced
The grade 7 fractions sequence covers complex fractions, signed fractions, and fractions as terminating and repeating decimals; this page sits inside it. What a student is asked to do here is grade 7 Complex Fractions and Unit Rates. Concretely, the sheet tests whether a student can read a situation and choose an operation before computing and work in fractional units and give the answer in lowest terms.
About the drill format
This drill runs 16 problems in a steady layout, so the eye never has to hunt for the next one; problem 6, "(3/8) ÷ (1/2)" shows the level it holds. A page of one fraction operation lets the renaming step become routine before anything else is layered on.
Set A, Set B and Set C
Set A is the original sheet, and Sets B and C were derived from it problem by problem: each number became a slot redrawn with the same shape, and every answer was recomputed exactly. Where Set A's problem 9 is "A runner covers 1/2 mile in 1/4 hour. What is the unit rate…", Set B's is "A machine finishes 7/8 of a part in 3/4 hour. What is the…".
8 story problem(s) drawn from the 7.RP.1 context family (unit rates from ratios of fractions) — parameters inferred from the standard and grade
How to use this worksheet
Have the student estimate before computing, then compare. At grade 7 an fractions answer that is wildly off should announce itself, and building that reflex matters as much as the sixteen answers. Ask the student to re-work one missed fractions problem from scratch on Set B rather than correcting it in place; the second attempt shows whether the method changed.
One mistake to watch for
Division of fractions inverts the wrong fraction, or both. Watch problem 1 of this drill — "(1/2) ÷ (1/4)" — for this one.
"Invert and multiply" is remembered as a rule without the reasoning that only the divisor flips.
Say "how many groups of the second fraction fit in the first" for a few problems, so the divisor is the one that changes.
Other grade 7 fractions formats
The same skill in the other formats available at this grade.
- Timed Drill — Grade 7 Fractions Timed Drill, 60 problems
- Missing Number — Grade 7 Fractions Missing Number, 24 problems
- Mixed Review — Grade 7 Fractions Mixed Review, 30 problems
- Word Problems — Grade 7 Fractions Word Problems, 10 problems
A step either side
The same format one grade down and one grade up — the easier sheet is often the faster fix when this one is not landing.
- Grade 6 Dividing Fractions — grade 6, 16 problems
Drill sheets in other grade 7 topics
Six PDFs, no sign-up: three versions of this grade 7 fractions drill and three answer keys, each sixteen problems long.