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B. Number · Operations: Numbers to 100 000, Decimals, Fractions, Ratios and Rates

Operations: Numbers to 100 000, Decimals, Fractions, Ratios and Rates: Unit Review

A1 B2.1 B2.2 B2.3 B2.4 B2.5 B2.6 B2.7 B2.8 B2.9About 40 minutes
Learning goals
  • I can use properties of operations, recall facts to 12 × 12, and do mental math with 0.1 and 0.01.
  • I can estimate, add and subtract whole numbers to 100 000 and decimals to hundredths.
  • I can add and subtract fractions with like denominators, and multiply and divide whole numbers by unit fractions.
  • I can multiply 2-digit by 2-digit numbers, divide 3-digit by 2-digit numbers, and use equivalent ratios and rates.

Words to know

partial product
One part of a multiplication, like 20 × 10 in 23 × 14.
quotient
The answer when you divide.
remainder
What is left over after dividing into equal groups. It is smaller than the divisor.
like denominators
Fractions with the same denominator, like 3/8 and 4/8.
unit fraction
A fraction with 1 as the numerator, like 1/4.
equivalent ratios
Ratios that make the same comparison, like 2:5 and 4:10.
unit rate
A rate for 1 of something, like 9 km per hour.

Let's review!

In this unit you became a powerful Grade 5 calculator and problem solver. You used properties to make math easier, learned facts to 12 × 12, multiplied by 0.1 and 0.01, estimated with decimals, added and subtracted big numbers and decimals, added and subtracted fractions, multiplied and divided with 2-digit numbers, made sense of remainders, solved multi-step problems, multiplied and divided by unit fractions, and worked with ratios and rates.

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.

3 × 1/43 ÷ 1/43 groups of one fourth= 3/4 (smaller than 3)123456789101112How many fourths fit in 3?= 12 (bigger than 3)
Same numbers, different questions. Multiplying by 1/4 takes part of each whole, so the answer is smaller. Dividing by 1/4 counts small pieces, so the answer is bigger.
Check with the partner operation+ and − undo each other47 386 + 28 759 = 76 14576 145 − 28 759 = 47 386× and ÷ undo each other336 ÷ 16 = 2116 × 21 = 336
Every addition has a matching subtraction, and every division has a matching multiplication. Use the partner to check your review answers.

Smart Strategies: Properties and Relationships of Operations

1

0.25 + 3.8 + 0.75 = ?

2

25 × 14 × 4 = ?

3

9 × 99 = ?

4

Check with addition: is 6.4 − 2.75 = 3.65 correct?

Multiplication Facts to 12 × 12

1

12 × 8 = ?

2

11 × 12 = ?

3

12 × 12 = ?

Division Facts and Fact Families to 144

1

108 ÷ 12 = ?

2

121 ÷ 11 = ?

3

Write the fact family for 6, 12 and 72.

Mental Math: Multiplying by 0.1 and 0.01

1

74 × 0.1 = ?

2

318 × 0.01 = ?

3

How many metres is 95 cm?

Estimating Sums and Differences of Decimals

1

Estimate 7.85 + 4.2.

2

Estimate 20.3 − 9.65.

3

Is 5.6 + 3.45 = 90.5 reasonable?

Adding and Subtracting Whole Numbers to 100 000

1

47 386 + 28 759 = ?

2

80 000 − 26 418 = ?

3

Check: is 63 210 − 27 845 = 35 365 correct?

Adding and Subtracting Decimals to Hundredths

1

6.78 + 2.57 = ?

2

9.1 − 4.36 = ?

3

You pay $20 for a $12.65 item. What's your change?

Adding and Subtracting Fractions with Like Denominators

1

3/10 + 5/10 = ?

2

7/8 − 3/8 = ?

3

4/5 + 3/5 = ? Write it as a mixed number.

4

1 − 5/12 = ?

Multiplying 2-Digit by 2-Digit Numbers: The Area Model

1

30 × 60 = ?

2

Use an area model: 26 × 13 = ?

3

A floor is 15 tiles by 24 tiles. How many tiles?

Multiplying 2-Digit by 2-Digit Numbers: The Algorithm

1

47 × 32 = ?

2

85 × 26 = ?

3

In 63 × 45, what does the second row stand for?

Dividing 3-Digit by 2-Digit Numbers: Area Model and Partial Quotients

1

336 ÷ 16 = ?

2

828 ÷ 36 = ?

3

420 students are split into teams of 15. How many teams?

Dividing 3-Digit by 2-Digit Numbers: The Long Division Algorithm

1

672 ÷ 21 = ?

2

805 ÷ 35 = ?

3

Check: is 918 ÷ 27 = 34 correct?

Remainders: What Should We Do with the Leftovers?

1

400 ÷ 18 = ?

2

170 campers ride buses that hold 40. How many buses are needed?

3

$150 is shared equally by 12 people. How much does each get?

Solving Multi-Step Problems and Checking Answers

1

4 boxes of 36 pencils are shared by 24 students. How many each?

2

You have $30. You buy 2 tickets at $8.75 each. How much is left?

3

A number divided by 25 gives 12 R7. What is the number?

Multiplying Whole Numbers by Unit Fractions

1

6 × 1/2 = ?

2

7 × 1/4 = ?

3

Each pancake uses 1/3 cup of batter. How much for 9 pancakes?

Dividing Whole Numbers by Unit Fractions

1

4 ÷ 1/2 = ?

2

3 ÷ 1/5 = ?

3

How many 1/4 cup scoops fill 2 cups?

Equivalent Ratios and Rates

1

Complete: 4:5 = 12:□.

2

Write 10:15 in simplest form.

3

A cyclist rides 24 km in 2 hours. How far in 5 hours at the same rate?

4

Which is the better buy: 2 for $3 or 5 for $7?

Just for fun

Riddle: Why was the math book so calm before the test?

It had already worked through all of its problems! Now it's your turn.

How to use this review

  • Do the review over two or three short sittings. Each section matches one lesson.
  • Estimate first, then check that your answer is close.
  • Use tools when you need them: grid paper, money, measuring cups, paper strips or a number line. Using tools is part of Grade 5 math.
  • Check with the inverse operation: addition for subtraction, multiplication for division.
  • Put a star next to any question you got wrong, and go back to that lesson's practice.
Check your understanding

Quiz

1.

What is 4 × 23 × 25?

2.

What is 12 × 7?

3.

What is 85 × 0.01?

4.

What is 52 816 + 29 475?

5.

What is 8.4 − 3.75?

6.

What is 5/9 + 2/9?

7.

What is 34 × 26?

8.

330 people ride buses that hold 48. How many buses are needed?

9.

What is 3 ÷ 1/3?

10.

Complete: 3:8 = 9:□.

For parents and teachers

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

  • Uses "any order" for subtraction, or fixes a friendly number the wrong way: revisit Smart Strategies: Properties and Relationships of Operations. Use flyer prices and look for friendly pairs.
  • Slow or unsure with the 11s and 12s: revisit Multiplication Facts to 12 × 12. Play multiplication war with Jacks (11) and Queens (12).
  • Can't turn a division fact into a multiplication fact: revisit Division Facts and Fact Families to 144. Practise with fact families.
  • Moves digits the wrong way or the wrong number of places with × 0.1 and × 0.01: revisit Mental Math: Multiplying by 0.1 and 0.01. Use dimes, cents and a metre stick.
  • Estimates by working out the exact answer first, or rounds using the wrong digit: revisit Estimating Sums and Differences of Decimals. Practise with a grocery receipt.
  • Misaligns digits or gets stuck regrouping across zeros in big numbers: revisit Adding and Subtracting Whole Numbers to 100 000. Use grid paper.
  • Lines up the last digits instead of the decimal points: revisit Adding and Subtracting Decimals to Hundredths. Use money.
  • Adds the denominators (2/8 + 3/8 = 5/16): revisit Adding and Subtracting Fractions with Like Denominators. Use folded paper strips.
  • Finds only two partial products, or writes 20 × 40 = 80: revisit Multiplying 2-Digit by 2-Digit Numbers: The Area Model. Draw it on grid paper.
  • Forgets the placeholder zero in the second row: revisit Multiplying 2-Digit by 2-Digit Numbers: The Algorithm. Compare each row with the area model.
  • Doesn't know where to start with a 2-digit divisor: revisit Dividing 3-Digit by 2-Digit Numbers: Area Model and Partial Quotients. Write a list of friendly multiples first.
  • Has trouble estimating each digit, or forgets to bring down: revisit Dividing 3-Digit by 2-Digit Numbers: The Long Division Algorithm. Let partial quotients be a back-up method.
  • Writes "5 R10 buses", or leaves a remainder bigger than the divisor: revisit Remainders: What Should We Do with the Leftovers?. Re-read the question before answering.
  • Stops after one step, or uses every number without thinking: revisit Solving Multi-Step Problems and Checking Answers. Draw a bar model.
  • Multiplies the denominator too (3 × 1/5 = 3/15): revisit Multiplying Whole Numbers by Unit Fractions. Use measuring cups.
  • Confuses 3 ÷ 1/4 with 3 × 1/4: revisit Dividing Whole Numbers by Unit Fractions. Cut paper strips and count the pieces.
  • Adds the same number to both terms of a ratio, or switches their order: revisit Equivalent Ratios and Rates. Make a ratio table.

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