Grade 7 Math practice

25 Grade 7 math lessons, including multiply and divide integers, rational numbers on a line, add positive and negative decimals, order rational numbers, combine like terms, match the simplified form and more. Each one has a short video where Pip explains the idea, a worked example, and endless new practice questions with step-by-step help when a child gets stuck.

Step 1: Multiply and divide integers

Multiply or divide the numbers, then work out the sign: same signs are positive, different signs are negative.

Example: 28 ÷ (−4)

Tip: A negative times a negative is a positive.

Step 2: Rational numbers on a line

Halves fit between the integers: −1.5 is halfway between −2 and −1.

Example: Tap 0.5 on the number line.

Tip: Each jump here is 0.5.

Step 3: Add positive and negative decimals

Add decimals with signs the same way as integers. Same signs: add. Different signs: subtract and keep the sign of the bigger one.

Example: 8.8 + 5.2

Tip: −2.5 + 4.1: the signs differ, so 4.1 − 2.5 = 1.6, and 4.1 is bigger, so the answer is positive.

Step 4: Order rational numbers

Rational numbers include negatives, fractions and decimals. Turn them into decimals to compare.

Example: Put these in order, least first.

Tip: −1.5 < −0.5 < 0.25 < 2/3.

Step 5: Combine like terms

Like terms have the same variable. 3x + 5x = 8x, just like 3 apples + 5 apples = 8 apples.

Example: 3x + 9 + 6x = ? x + 9

Tip: Add or subtract the numbers in front of x. Leave plain numbers alone.

Step 6: Match the simplified form

Combine like terms: 3x + 2x = 5x. Numbers combine with numbers.

Example: Match each expression to its simplified form.

Tip: Add the x terms, then the numbers.

Step 7: Spot the like term

Like terms have the same variable to the same power: 3x and 4x are like terms.

Example: Tap the term that is a like term with 5x.

Tip: Look for the same letter, with no other letters.

Step 8: The distributive property

Multiply the number outside the brackets by each term inside: 3(x + 4) = 3x + 12.

Example: 9(x + 7) = 9x + ?

Tip: Draw arrows from the outside number to each term inside.

Step 9: Brackets first

For 3(4 + 5), you can add first or multiply each term: 3 × 4 + 3 × 5.

Example: Build the value of 5(4 + 5).

Tip: Both ways give the same answer.

Step 10: Two-step equations

Undo the operations in reverse order: first undo adding or subtracting, then undo multiplying.

Example: 4 x + 18 = 22

Tip: Whatever you do to one side, do to the other side too.

Step 11: Solve inequalities

Solve an inequality like an equation: do the same thing to both sides.

Example: 5x > 35 → x > ?

Tip: x + 5 > 12 → subtract 5 from both sides → x > 7.

Step 12: Make it true

An inequality has many solutions. x + 4 > 9 is true for any x bigger than 5.

Example: Choose every value that makes x + 4 > 8 true.

Tip: Solve it like an equation, then think "bigger or smaller".

Step 13: Proportions

A proportion says two ratios are equal. Find what one side was multiplied by, and do the same to the other.

Example: 9/9 = 18/ ?

Tip: Cross-multiplying also works: the two diagonal products are equal.

Step 14: Scale drawings

A scale tells how drawing lengths match real lengths. 1 cm : 5 m means each cm on the drawing is 5 m in real life.

Example: On a map, 1 cm : 10 m . A path on the map is 10 cm long. How long is the real path, in m?

Tip: Multiply the drawing length by the scale.

Step 15: Sales and discounts

A discount is a percent taken off the price. Find the discount, then subtract it.

Example: A backpack costs $180. It is 50% off. What is the sale price in dollars?

Tip: 25% off means you pay 75% of the price.

Step 16: Same as 75%?

One amount can look different: 3/4 = 0.75 = 75%.

Example: Is each one equal to 75%?

Tip: Turn each one into a percent.

Step 17: Tips and taxes

A tip or tax is a percent of the price. 15% of $40 = 0.15 × 40 = $6.

Example: A meal costs $35 . The tax is 10% . How much is the tax, in dollars?

Tip: Find 10% first (move the decimal one place), then build up.

Step 18: Simple interest

Simple interest = principal × rate × time. Money saved at 3% a year earns 3% of it each year.

Example: You save $200 at 2% simple interest per year for 2 years. How much interest do you earn, in dollars?

Tip: Find one year of interest, then multiply by the number of years.

Step 19: Percent increase

Percent change = change ÷ original × 100.

Example: A price goes from $25 to $30. What is the percent increase? (like 20%)

Tip: From 40 to 50 is a change of 10. 10 ÷ 40 = 25%.

Step 20: Angles in a triangle

The three angles of any triangle add up to 180°.

Example: Find the missing angle. 30° + 117° + ? = 180°

Tip: Add the two angles you know, then subtract from 180.

Step 21: True or false: angles

Angles on a straight line add to 180°. Angles in a triangle add to 180°.

Example: Is this true or false? A triangle can have two right angles.

Tip: Right angles are 90°.

Step 22: Circumference of circles

The distance around a circle is π × diameter. π is about 3.14.

Example: A circle has a radius of 9 cm. What is its circumference? Use π ≈ 3.14.

Tip: The diameter is twice the radius.

Step 23: Area of circles

Area of a circle = π × r × r. Use 3.14 for π.

Example: A circle has radius 4 cm. What is its area in cm²? (Use 3.14 for π.)

Tip: Square the radius first, then multiply by 3.14.

Step 24: Probability

Probability = the outcomes you want ÷ all the possible outcomes.

Example: A bag has 6 red, 3 blue marbles. You pick one without looking. What is the probability it is red? ? /9

Tip: A probability is always between 0 (impossible) and 1 (certain).

Step 25: Make the probability

Probability = favourable outcomes ÷ all outcomes.

Example: Shade sections so the chance of landing on blue is 1/8.

Tip: For 3/8: shade 3 of 8 equal sections.

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