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B. Number · Operations: Divisibility, Decimals, Fractions, Ratios and Percents

Operations: Divisibility, Decimals, Fractions, Ratios and Percents: Unit Review

A1 B2.1 B2.2 B2.3 B2.4 B2.5 B2.6 B2.7 B2.8 B2.9 B2.10 B2.11 B2.12About 40 minutes
Learning goals
  • I can use the order of operations, properties, divisibility rules and prime factorization.
  • I can find percents mentally and solve ratio, rate and percent problems.
  • I can add and subtract whole numbers, decimals, fractions and mixed numbers.
  • I can multiply and divide with decimal tenths, divide decimals by whole numbers, and multiply and divide whole numbers by proper fractions.

Words to know

order of operations
Brackets first, then × and ÷ from left to right, then + and − from left to right.
divisible
Divides with no remainder.
prime number
A whole number greater than 1 with exactly two factors: 1 and itself.
common denominator
A denominator two fractions can share, like 12 for 1/4 and 1/6.
unit rate
A rate for one unit, like 80 km per hour.
percent
A ratio that compares a number to 100.

Let's review!

In this unit you used the order of operations and properties, learned divisibility rules and factor trees, found percents in your head, added and subtracted big numbers and decimals, added and subtracted fractions and mixed numbers, multiplied and divided with decimal tenths, divided decimals by whole numbers, multiplied and divided whole numbers by fractions, solved ratio, rate and percent problems, and put it all together in multi-step problems.

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.

Will the answer be bigger or smaller?× by a number less than 1÷ by a number less than 1SMALLERBIGGER324 × 0.7 = 226.8240 ÷ 0.6 = 4003/4 × 12 = 96 ÷ 3/4 = 84 × 2/3 = 2 2/34 ÷ 2/3 = 6
A quick estimate check: multiplying by a number less than 1 makes the answer smaller; dividing by a number less than 1 makes it bigger.
Where to look: is 5240 divisible by...?5240last digit0 → 2, 5 and 10 ✓last two digits40 ÷ 4 = 10 → 4 ✓last three digits240 ÷ 8 = 30 → 8 ✓digit sum5 + 2 + 4 + 0 = 11 → not 3, 6 or 9
Each rule looks at a different part of the number. 5240 passes the tests for 2, 4, 5, 8 and 10, but its digit sum (11) fails the tests for 3, 6 and 9.

Properties and the Order of Operations

1

7 + 6 × 3 = ?

2

(7 + 6) × 3 = ?

3

40 − 18 ÷ 3 × 2 = ?

4

4 × 2.5 × 9 = ?

Divisibility Rules for 2, 4, 5, 8 and 10

1

Is 3 724 divisible by 4?

2

Is 5 216 divisible by 8?

3

Is 4 570 divisible by 2, 5 and 10?

4

Is 1 238 divisible by 4?

Divisibility Rules for 3, 6 and 9

1

Is 2 457 divisible by 9?

2

Is 1 734 divisible by 6?

3

Is 5 203 divisible by 3?

Prime Numbers, Composite Numbers and Factor Trees

1

Is 37 prime or composite?

2

Write 56 as a product of prime factors.

3

Write 150 as a product of prime factors.

4

Write 63 as a product of prime factors.

Mental Math with Percents

1

10% of 470 = ?

2

15% of 120 = ?

3

25% of 64 = ?

4

1% of 900 = ?

Adding and Subtracting Whole Numbers and Decimals

1

562 418 + 279 695 = ?

2

700 000 − 248 563 = ?

3

8.4 − 2.765 = ?

4

3.08 + 12.5 + 0.476 = ?

Adding and Subtracting Fractions with Unlike Denominators

1

1/3 + 1/4 = ?

2

5/6 − 1/2 = ?

3

3/5 + 1/2 = ?

Adding and Subtracting Mixed Numbers

1

1 2/3 + 2 1/2 = ?

2

5 1/4 − 1 2/3 = ?

3

4 − 2 5/8 = ?

Multiplying Whole Numbers by Decimal Tenths

1

236 × 0.4 = ?

2

125 × 3.2 = ?

3

408 × 2.5 = ?

Dividing Whole Numbers by Decimal Tenths

1

280 ÷ 0.7 = ?

2

384 ÷ 1.2 = ?

3

250 m of rope is cut into 0.6 m pieces. How many pieces? How much is left?

Dividing Decimals by Whole Numbers

1

9.72 ÷ 4 = ?

2

5.4 ÷ 8 = ?

3

Six people share a $31.50 bill equally. How much each?

Multiplying Whole Numbers by Proper Fractions

1

3/4 of 28 = ?

2

6 × 3/5 = ?

3

5/6 of 42 = ?

Dividing Whole Numbers by Proper Fractions

1

6 ÷ 3/4 = ?

2

4 ÷ 2/5 = ?

3

3 ÷ 2/3 = ?

Solving Problems with Ratios and Rates

1

4:5 = ?:35

2

A bus goes 270 km in 3 hours. How far in 7 hours at the same speed?

3

Write 18:24 in simplest form.

4

Which is the better buy: 3 muffins for $4.50 or 5 muffins for $7.00?

Solving Problems with Percents

1

Write 11 out of 20 as a percent.

2

A $60 sweater is 15% off. What is the sale price?

3

What is the total for a $50 item with 13% HST?

Solving Multi-Step Problems

1

3 pizzas cost $14.75 each, plus $4 delivery. 5 friends share the cost equally. How much does each pay?

2

200 − 5 × (12 + 8) = ?

3

45 students are in a winter club. 2/3 of them go skating. 20% of the skaters bring their own skates. How many bring their own skates?

Just for fun

Why was 6 afraid of 7?

Because 7 8 9! (Don't worry: 7 is a prime number, so it can only be divided evenly by 1 and itself. It isn't interested in anyone else.)

How to use this review

  • Do the review over two or three short sittings. Each section matches one lesson.
  • Estimate first, so you know about how big the answer should be and where the decimal point goes.
  • Use tools when you need them: measuring cups, paper strips, money, a number line or a calculator for checking.
  • 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 12 + 8 ÷ 4?

2.

Which number is divisible by 9?

3.

What is the prime factorization of 60?

4.

What is 15% of 80?

5.

What is 4.2 − 1.375?

6.

What is 2 1/2 + 1 2/3?

7.

What is 312 × 0.5?

8.

What is 150 ÷ 0.3?

9.

What is 8 ÷ 2/3?

10.

What is 12 out of 15 as a percent?

For parents and teachers

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

  • Works left to right without doing brackets or × and ÷ first: revisit Properties and the Order of Operations. Play the card target game.
  • Thinks every even number is divisible by 4, or checks only the last digit for 8: revisit Divisibility Rules for 2, 4, 5, 8 and 10.
  • Uses the digit sum for 6 without checking that the number is even: revisit Divisibility Rules for 3, 6 and 9.
  • Calls 1 prime, or leaves a composite number (like 4 or 9) at the end of a factor tree: revisit Prime Numbers, Composite Numbers and Factor Trees.
  • Divides by 5 to find 5%, or moves digits the wrong way for 10% and 1%: revisit Mental Math with Percents. Use flyer prices.
  • Lines up the last digits instead of the decimal points, or struggles regrouping across zeros: revisit Adding and Subtracting Whole Numbers and Decimals.
  • Adds the denominators (1/2 + 1/3 = 2/5): revisit Adding and Subtracting Fractions with Unlike Denominators. Use measuring cups or paper strips.
  • Leaves answers like 3 5/4, or doesn't regroup a whole when subtracting: revisit Adding and Subtracting Mixed Numbers.
  • Puts the decimal point in the wrong place when multiplying by tenths: revisit Multiplying Whole Numbers by Decimal Tenths. Estimate first.
  • Multiplies only one number by 10 when dividing by tenths, or misreads the remainder: revisit Dividing Whole Numbers by Decimal Tenths. Use dimes.
  • Misplaces the decimal point or stops with a remainder when dividing decimals: revisit Dividing Decimals by Whole Numbers.
  • Multiplies the denominator too (3 × 3/4 = 9/12): revisit Multiplying Whole Numbers by Proper Fractions. Use small objects in equal groups.
  • Confuses 4 ÷ 2/3 with 4 × 2/3: revisit Dividing Whole Numbers by Proper Fractions. Use measuring cups and ask "How many fit?"
  • Adds the same number to both terms of a ratio, or mixes up part-to-part and part-to-whole: revisit Solving Problems with Ratios and Rates. Make a ratio table.
  • Gives the discount instead of the sale price, or thinks 18 out of 25 is 18%: revisit Solving Problems with Percents.
  • Stops after one step, or doesn't check whether the answer is reasonable: revisit Solving Multi-Step Problems. Use the four-step plan.

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