Grade by Grade
B. Number · Operations: Exponents, Factors, Fractions, Decimals, Integers, Percents and Proportions

Operations: Exponents, Factors, Fractions, Decimals, Integers, Percents and Proportions: Unit Review

A1 B2.1 B2.2 B2.3 B2.4 B2.5 B2.6 B2.7 B2.8 B2.9 B2.10About 40 minutes
Learning goals
  • I can use exponents, the order of operations and properties of operations.
  • I can find the GCF and LCM, and add, subtract, multiply and divide fractions.
  • I can multiply and divide decimals, and add and subtract integers.
  • I can recall common percent equivalents, change numbers by a percent, and use proportional reasoning.

Words to know

exponent
Tells how many times the base is used as a factor: 2³ = 2 × 2 × 2.
BEDMAS
Brackets, Exponents, Division and Multiplication, Addition and Subtraction.
GCF
The greatest common factor: the largest number that divides all the numbers.
LCM
The lowest common multiple: the smallest number all the numbers divide into.
reciprocal
A fraction flipped: the reciprocal of 2/3 is 3/2.
zero pair
(+1) + (−1) = 0.
proportional
When the ratio between two quantities always stays the same.

Let's review!

In this unit you learned to use exponents and the full order of operations, found the GCF and LCM, added, subtracted, multiplied and divided fractions, multiplied and divided decimals by decimals, added and subtracted integers, learned common percent equivalents, increased and decreased numbers by percents, and used proportional reasoning.

This review has a few questions from every lesson. Try each one, then press Show answer to check. If a part feels tricky, go back to that lesson for more practice.

Splitting into equal groups?→ GCF12 = 2 × 2 × 318 = 2 × 3 × 3shared primes: 2 × 3GCF(12, 18) = 6Waiting to line up again?→ LCM12 = 2² × 318 = 2 × 3²most of each prime: 2² × 3²LCM(12, 18) = 36
Quick reminder: the GCF is never bigger than the smaller number, and the LCM is never smaller than the bigger number.
−5−4−3−2−10+1+2+3+4+5(−2) − (+3) = (−2) + (−3) = −5move 3 leftSubtracting is the same as adding the opposite.
To subtract an integer, add its opposite. Start at −2 and move 3 to the left to land on −5.

Exponents: Repeated Multiplication

1

Find the value of 2⁵.

2

Write 9 × 9 × 9 × 9 in exponential form.

3

Write the prime factorization of 108 using exponents.

The Order of Operations with Exponents

1

4 + 3² × 2 = ?

2

(4 + 3)² − 9 = ?

3

Use a property to find 25 × 48 in your head.

The Greatest Common Factor

1

Find the GCF of 28 and 42.

2

Find the GCF of 24, 60 and 84.

3

Use the GCF to write 45/75 in lowest terms.

The Lowest Common Multiple

1

Find the LCM of 6 and 15.

2

Find the LCM of 4, 9 and 12.

3

Two buses leave together. One returns every 12 minutes, the other every 16 minutes. When are they next together?

Adding and Subtracting Fractions

1

3/4 + 5/6 = ?

2

7/10 − 1/4 = ?

3

5 1/6 − 2 3/4 = ?

Multiplying Fractions by Fractions

1

3/5 × 5/6 = ?

2

2/3 of 9/10 = ?

3

1 1/3 × 2 1/4 = ?

Dividing Fractions by Fractions

1

5/6 ÷ 1/12 = ?

2

3/8 ÷ 3/4 = ?

3

How many 3/4 cup servings are in 4 1/2 cups of soup?

Multiplying Decimals by Decimals

1

0.8 × 0.6 = ?

2

2.3 × 1.4 = ?

3

Fish costs $18.50 per kg. How much is 0.4 kg?

Dividing Decimals by Decimals

1

4.2 ÷ 0.7 = ?

2

0.81 ÷ 0.09 = ?

3

A 1.5 kg bag of rice costs $5.25. What is the price per kilogram?

Adding Integers

1

(−9) + (+4) = ?

2

(−6) + (−7) = ?

3

The temperature is −14°C and rises 20 degrees. What is the new temperature?

Subtracting Integers

1

(+2) − (+9) = ?

2

(−3) − (−10) = ?

3

The temperature drops from +4°C to −9°C. What is the change?

Percents, Fractions and Decimals to Know by Heart

1

Write 3/8 as a decimal and a percent.

2

Write 4% as a fraction in lowest terms.

3

Find 66 2/3% of 48.

Increasing and Decreasing by a Percent in Your Head

1

Increase 120 by 25%.

2

Decrease 80 by 5%.

3

Increase 45 by 100%.

Proportional and Non-Proportional Situations

1

Is this proportional? x: 2, 5, 8 and y: 6, 15, 24.

2

An arena charges $5 entry plus $2 per hour for skate rental. Is the total cost proportional to the number of hours?

3

6 muffins cost $9. How much do 10 muffins cost?

Just for fun

Why was the equal sign so humble?

It knew it wasn't greater than or less than anyone else.

How to use this review

  • Work through one section at a time and write your steps, not just the answers.
  • Put a check mark beside each question you got right on your own. Put a star beside any you needed help with.
  • If you starred two or more questions in a section, go back to that lesson and redo its "More practice" questions.
  • Finish with the quiz. For every quiz mistake, read the explanation and find the lesson it came from.
  • Mistakes are useful: they show exactly what to practise next.
Check your understanding

Quiz

1.

What is 3 + 2⁴ ÷ 8?

2.

What is the GCF of 36 and 54?

3.

What is the LCM of 8 and 10?

4.

What is 2/3 + 1/4?

5.

What is 3/4 × 2/5?

6.

What is 3/5 ÷ 1/10?

7.

What is 1.6 ÷ 0.04?

8.

What is (−5) − (−8)?

9.

Decrease 60 by 25%.

10.

Which situation is proportional?

For parents and teachers

Use mistakes to choose what to revisit. Each review section matches one lesson.

  • Multiplies the base by the exponent (2⁵ = 10): revisit Exponents: Repeated Multiplication. Redo the paper-folding activity.
  • Works left to right without doing brackets and exponents first, or squares after multiplying: revisit The Order of Operations with Exponents.
  • Multiplies all the prime factors, or gives a common factor that isn't the greatest: revisit The Greatest Common Factor.
  • Always multiplies the two numbers, or mixes up GCF and LCM: revisit The Lowest Common Multiple.
  • Adds the denominators, or regroups mixed numbers incorrectly: revisit Adding and Subtracting Fractions.
  • Finds a common denominator to multiply, or multiplies mixed numbers part by part: revisit Multiplying Fractions by Fractions.
  • Flips the wrong fraction, or expects division to always give a smaller answer: revisit Dividing Fractions by Fractions. Use measuring cups.
  • Misplaces the decimal point in a product: revisit Multiplying Decimals by Decimals. Estimate first.
  • Multiplies only the divisor by 10 or 100: revisit Dividing Decimals by Decimals. Use coins.
  • Gets the sign wrong when adding a positive and a negative: revisit Adding Integers. Use zero pairs.
  • Thinks subtracting always gives a smaller number, or changes the wrong sign: revisit Subtracting Integers.
  • Thinks 1/8 = 0.8 or 1/5 = 15%: revisit Percents, Fractions and Decimals to Know by Heart. Play the memory game.
  • Gives the percent instead of the new amount, or thinks +10% then −10% gets back to the start: revisit Increasing and Decreasing by a Percent in Your Head.
  • Scales a situation that has a fixed fee or fixed difference: revisit Proportional and Non-Proportional Situations.

A few mistakes are normal. Praise the strategy your child explains and the habit of checking, not only the right answer.