23 problems graded by difficulty (★ easy, ★★ medium, ★★★ hard). Try first, without looking at the solutions!
2 Dividing integers ★★★
Compute. a) \(-48\div 6\) b) \(-56\div(-7)\) c) \(45\div(-9)\) d) \(0\div(-13)\)
3 Missing numbers ★★★
Find the missing integer. a) \((-5)\cdot\square=35\) b) \(\square\div(-4)=9\) c) \(72\div\square=-8\)
4 Multiplying fractions ★★★
Compute and simplify. a) \(\dfrac{2}{5}\cdot\dfrac{3}{7}\) b) \(\dfrac{3}{4}\cdot\dfrac{8}{15}\) c) \(-\dfrac{1}{2}\cdot\dfrac{6}{7}\)
5 Reciprocals ★★★
Write the reciprocal of each number. a) \(\dfrac{3}{8}\) b) \(-5\) c) \(2\dfrac{1}{2}\)
6 Fractions to decimals ★★★
Write each fraction as a decimal. Use a bar for repeating digits. a) \(\dfrac{3}{8}\) b) \(\dfrac{7}{20}\) c) \(\dfrac{5}{6}\) d) \(\dfrac{2}{9}\)
7 True or false? ★★★
True or false? Justify. a) The product of two negative numbers is negative. b) \(-12\div(-3)\) is positive. c) The reciprocal of \(-\dfrac{2}{3}\) is \(\dfrac{3}{2}\).
8 Milk for pancakes ★★★
One batch of pancakes needs \(\dfrac{3}{4}\) liter of milk. How much milk do \(2\dfrac{2}{3}\) batches need?
9 Mixed number division ★★★
Compute. a) \(3\dfrac{1}{2}\div 1\dfrac{3}{4}\) b) \(-2\dfrac{2}{5}\div\dfrac{3}{10}\)
10 Integer order of operations ★★★
Evaluate. a) \(-3+4(-5+2)^2\) b) \(18\div(-3)\cdot 2-(-4)\)
11 Terminate or repeat? ★★★
Without dividing, decide which fractions give terminating decimals: \(\dfrac{7}{8}\), \(\dfrac{5}{12}\), \(\dfrac{11}{25}\), \(\dfrac{4}{21}\). Explain.
12 Repeating blocks ★★★
Use long division to write as repeating decimals. a) \(\dfrac{4}{15}\) b) \(\dfrac{5}{7}\) c) \(\dfrac{7}{12}\) d) \(\dfrac{4}{11}\)
13 Distributive shortcuts ★★★
Use the distributive property to compute mentally. a) \(15\left(-\dfrac{2}{5}+\dfrac{1}{3}\right)\) b) \(24\left(\dfrac{5}{6}-\dfrac{3}{8}\right)\)
14 Freezer ★★★
A freezer starts at \(14^\circ\)F and its temperature changes by \(-2.5^\circ\)F every hour for 6 hours. What is the final temperature?
15 Find the error ★★★
A student wrote \(-\dfrac{2}{3}\div\dfrac{4}{9}=-\dfrac{8}{27}\). Explain the mistake and give the right answer.
16 Name the property ★★★
Name the property. a) \(7\cdot(-4)=(-4)\cdot 7\) b) \((2\cdot(-3))\cdot 5=2\cdot((-3)\cdot 5)\) c) \(-9\cdot 1=-9\) d) \(\dfrac{5}{6}\cdot\dfrac{6}{5}=1\) e) \(4(x+3)=4x+12\)
17 Bank balance ★★★
Dana’s account has 60 dollars. Each week 18.50 dollars are withdrawn automatically for 7 weeks with no deposits. What is the balance?
18 Rain barrel ★★★
A 60-gallon barrel is \(\dfrac{5}{6}\) full. Then \(\dfrac{3}{10}\) of the water is poured into buckets that each hold \(2\dfrac{1}{2}\) gallons. How many buckets are filled?
19 Mean of changes ★★★
Five mornings at a ski resort were \(-3.5\), \(2\), \(-1.25\), \(0.75\) and \(-4\) degrees F relative to freezing. Find the mean.
20 A big expression ★★★
Evaluate. a) \(\dfrac{-\frac{3}{4}+\frac{5}{6}}{-\frac{1}{3}}\) b) \(2\dfrac{1}{2}\cdot\left(-\dfrac{4}{5}\right)-(-3)^2\div(-6)\)
21 Odd and even ★★★
a) Compute \((-1)^{15}\), \((-1)^{20}\) and \((-2)^5\). b) Without a calculator, find the sign and value of \((-2)(-3)(-1)(-5)(-1)(-2)(-4)\). Explain your reasoning.
22 Ordering mixed forms ★★★
Order from least to greatest: \(\dfrac{5}{7}\), \(0.7\), \(\dfrac{8}{11}\), \(0.\overline{7}\). Show the decimal values.
23 Reading rate ★★★
Maya reads \(3\dfrac{1}{2}\) pages in \(\dfrac{1}{4}\) hour. a) How many pages per hour? b) At that rate, how long does a 49-page chapter take?
Test yourself: quick challenge for Grade 7
Speed drill for Grade 7: how many in 60 seconds?
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