Key takeaway: This grade 7 rational number operations worksheet gives 20 printable problems on converting fractions to decimals and on computing with positive and negative rational numbers. Students use long division, order numbers on a line, add and subtract fractions, and finish with temperature, bank, elevation, and stock stories. An answer key on its own page lets families check every line.
The set moves from terminating decimals to repeating decimals and then to operations. Because the last problems chain several steps, the order of the sheet matters.
These 20 problems practice standards 7.NS.A.2d and 7.NS.A.3: writing rational numbers as terminating or repeating decimals by long division, and solving real-world problems that use all four operations with fractions, decimals and negative numbers. The last seven are multi-step problems about temperature, money, elevation, water, and stock prices.
Grade 7 Rational Number Operations Worksheet: problems 1–5
1. Fractions to decimals
Use long division to write each fraction as a decimal.
- \(\frac{3}{5}\)
- \(\frac{7}{8}\)
- \(\frac{9}{20}\)
2. Long division to decimals
Use long division to write each fraction as a decimal.
- \(\frac{9}{25}\)
- \(\frac{11}{16}\)
- \(\frac{13}{40}\)
3. Repeating decimals
Use long division to write \(\frac{2}{3}\) and \(\frac{5}{6}\) as decimals. Use a bar to show the repeating digits.
4. Repeating digits
Use long division to write each fraction as a decimal. Use a bar to show the repeating digits.
- \(\frac{5}{9}\)
- \(\frac{7}{12}\)
- \(\frac{4}{11}\)
5. Terminate or repeat
Without a calculator, decide whether each fraction is a terminating or a repeating decimal. Write the decimal.
- \(\frac{7}{20}\)
- \(\frac{4}{9}\)
- \(\frac{11}{12}\)
- \(\frac{9}{16}\)
Grade 7 Rational Number Operations Worksheet: problems 6–10
6. Mixed numbers
Write each rational number as a decimal.
- \(2\frac{3}{8}\)
- \(-3\frac{5}{6}\)
- \(1\frac{7}{20}\)
7. Negative fractions
Write each number as a decimal.
- \(-\frac{7}{11}\)
- \(-\frac{13}{8}\)
8. Add and subtract decimals
Evaluate.
- \(-6.4+9.75\)
- \(2.8-(-4.15)\)
- \(-7.25-3.6\)
- \(-0.75-(-1.5)\)
9. Order on a number line
Write the numbers in order from least to greatest: \(0.6,\ -\frac{3}{4},\ \frac{5}{8},\ -0.7\).
10. Ordering mixed forms
Write the numbers in order from least to greatest: \(\frac{1}{4},\ -0.3,\ 0.2,\ -\frac{1}{3},\ -0.35\).
Grade 7 Rational Number Operations Worksheet: problems 11–15
11. Four operations
Evaluate.
- \(-3.5+2.25\)
- \(\frac{3}{4}-(-\frac{1}{2})\)
- \((-\frac{2}{3})(\frac{9}{10})\)
- \((-\frac{5}{6}): (-\frac{5}{12})\)
12. Add and subtract fractions
Evaluate. Write each answer as a fraction or mixed number in lowest terms.
- \(-\frac{2}{5}+\frac{3}{4}\)
- \(\frac{5}{6}-(-\frac{1}{3})\)
- \(-\frac{3}{8}-\frac{1}{2}\)
- \(-1\frac{1}{2}+2\frac{1}{4}\)
13. Multiply and divide
Evaluate.
- \((-1.5)(-4.2)\)
- \((-\frac{3}{5})(\frac{10}{9})\)
- \((-12.6): 3\)
- \(\frac{7}{8}: (-\frac{7}{4})\)
14. Temperature rise
At 6 AM the temperature was \(-8.5^{\circ}\text{F}\). It rose \(3.25^{\circ}\text{F}\) each hour for 4 hours. Find the temperature at 10 AM.
15. Account balance
Jamal's account starts at $42.50. He spends $18.75, deposits $25.20, then spends $31.95. Find his final balance.
Grade 7 Rational Number Operations Worksheet: problems 16–20
16. Death Valley hike
Ethan starts a hike at an elevation of \(-150.5\) feet, which is below sea level. He walks down 3 steep sections, each \(42.25\) feet, and then climbs up \(60.5\) feet.
- Find the total change in elevation for the 3 steep sections.
- Find his elevation after the 3 sections.
- Find his final elevation after the climb.
17. Diver depth
A diver is at \(-36\frac{1}{2}\) ft. She descends \(14\frac{3}{4}\) ft and then rises \(8.25\) ft. Find her final depth.
18. Draining tank
A water tank holds 24 gallons. A leak lowers the amount of water by \(2\frac{1}{4}\) gallons each hour, and the change is \(-2\frac{1}{4}\) gallons per hour.
- Find the total change in the amount of water after 6 hours.
- Find the amount of water left after 6 hours.
- Find how many hours it takes for the tank to empty. Write the answer as a decimal with a bar.
19. Rate of change
The temperature dropped from \(14.5^{\circ}\text{F}\) to \(-6.5^{\circ}\text{F}\) in 6 hours at a constant rate.
- Find the total change.
- Find the change per hour.
- Find the temperature after 4 hours.
20. Share price
A share of a company's stock costs $27.80. Over the next 6 days it changes by \(-\$0.35\) each day. Over the following 4 days it changes by \(+\$1.25\) each day.
- Find the price after the 6 days.
- Find the price after the following 4 days.
- Find the net change in the price over all 10 days.
What do the first decimal problems ask?
First, Problem 1 turns 3/5, 7/8, and 9/20 into decimals by long division. Next, Problem 2 repeats the task with 9/25, 11/16, and 13/40. Then Problem 3 introduces 2/3 and 5/6, whose digits repeat, so students must write a bar. Later, Problem 5 asks them to predict without a calculator whether a fraction terminates.
How do you handle signs on a grade 7 rational number operations worksheet?
Problem 8 mixes four sums and differences, such as negative 6.4 plus 9.75. Problem 11 brings in fractions, and Problem 12 asks for lowest terms. Because subtraction means adding the opposite, rewrite each difference first. Then Problem 13 multiplies and divides, where equal signs give positive results.
How do ordering problems work?
Problem 9 lists 0.6, negative 3/4, 5/8, and negative 0.7, and students arrange them from least to greatest. Convert everything to decimals so the comparison is easy. As a result, negative 0.75 sits at the far left. Problem 10 repeats the idea with mixed forms.
Which word problems close the sheet?
The morning temperature of negative 8.5 degrees in Problem 14 rises 3.25 degrees an hour for four hours. In Problem 15, Jamal’s account starts at $42.50 and goes through three transactions. Ethan’s Death Valley hike in Problem 16 starts below sea level, and Problem 17 sends a diver below negative 36 and one half feet. Finally, Problem 19 asks for a rate of change.
Check the sheet with estimates
Before you accept an answer, estimate it with whole numbers. For example, negative 6.4 plus 9.75 should land near 3, so 3.35 makes sense. Also compare the sign of each result with a quick mental picture. Finally, redo any problem where the estimate and the answer disagree.
Printable PDF · Worksheet
Grade 7 Rational Numbers: Decimals, Fractions and Word Problems worksheet
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