Full Grade 5 test

Divide the whole amount by the denominator to find one equal part. Multiply that amount by the numerator. This gives the used length. Subtract it from the original length to find the remainder.

Multiply by the units digit and by the tens digit. Multiply the tens partial product by 10, then add the two partial products.

The numerator is above the fraction bar and counts the equal parts taken. The denominator is below it and counts the equal parts in the whole. In 3/5, the numerator 3 means three parts are taken.

Central symmetry about O is equivalent to a 180° rotation. The point O(5, 5) must be the midpoint of the segment joining the original point and its image.

1. Find the distance of the original x-coordinate from 5.
2. Move the same distance to the other side of the centre. The new x-coordinate is 10 − x.
3. Do the same for the y-coordinate. The new y-coordinate is 10 − y.

Answer form: A′(10 − x, 10 − y).

Work inside brackets first, then multiply and divide, and finally add and subtract. Perform operations of equal priority from left to right. Select the operation inside the brackets. You do not need to calculate the final value.

Rectangle area is S = length × width. Use the same units for both lengths. If the lengths are in centimetres, express the area in cm².

The mean shows what each value would be if the total of all bars were shared equally.

1. Read the value of each bar from the vertical scale.
2. Add all the values you read.
3. Divide the total by the number of bars.

Check that the mean lies between the smallest and largest values shown in the chart.

Convert both Roman numerals to ordinary numbers. Perform the indicated addition or subtraction, then convert the result back. I = 1, V = 5, X = 10, L = 50, C = 100; IV = 4, IX = 9, XL = 40, XC = 90. For example, VIII + IV = 8 + 4 = 12 = XII.

A number is divisible by 9 if and only if the sum of its digits is divisible by 9.

1. Add all the known digits of the number.
2. Find what is needed to reach the next multiple of 9.
3. Insert one digit so that the complete digit sum becomes a multiple of 9.

Check the result by adding all digits again. If the sum is 9, 18, 27 and so on, the divisibility rule for 9 is satisfied.

A frequency tells how many times a value occurred. The value that occurred most often is called the mode.

1. Compare the frequencies listed under A, B, C and D.
2. Find the largest frequency.
3. Choose the letter above that frequency, not the frequency number itself.

You do not need to add the frequencies or calculate their mean.

Work inside brackets first, then multiply and divide, and finally add and subtract. Perform operations of equal priority from left to right. Find the bracketed sum, divide it, then add the final number.

Probability equals the number of favourable equally likely outcomes divided by the total number of outcomes. The even die results are 2, 4 and 6, so three of the six outcomes qualify: 3/6 = 1/2 = 50%.

Read each bar value from the numbered axis. Add all the values, counting each one exactly once.

Convert each Roman numeral to an ordinary number and compare the values. I = 1, V = 5, X = 10, L = 50, C = 100. Subtract a smaller numeral before a larger one; otherwise add. The number of symbols does not determine the value: IX = 9, while VIII = 8.

Subtract the smaller number from the larger. Alternatively, count the gaps between A and B and multiply by the value of one gap. The number of ticks or gaps alone is not the distance in units.

A quarter turn is 90°, a half turn is 180° and three quarters is 270°. Clockwise directions follow this order: up → right → down → left → up. Count the required quarter turns.

Each kebab contains one choice of meat, one choice of salad and one choice of sauce.

1. Each type of meat can be paired with every salad choice.
2. Each resulting pair can be combined with every sauce.
3. Therefore, multiply the numbers of all three choices.

Rule: number of meat types × number of salad choices × number of sauces.

Equivalent fractions are formed by multiplying both numerator and denominator by the same number. Divide the new denominator by the old one and multiply the old numerator by that factor. For example, 2/3 = 8/12 because both numbers were multiplied by 4.

Subtract the left-hand labelled number from the right-hand one. Divide the difference by the number of equal gaps between them. Count gaps, not ticks: there is one fewer gap than the number of ticks bounding them.

The interior angles of a triangle total 180°. Add the two known angles and subtract their sum from 180°. Third angle = 180° − first angle − second angle.

Starting from the left, take the shortest dividend prefix at least as large as the divisor. Find a quotient digit, multiply, subtract and bring down the next digit. Repeat. Check: divisor × quotient = dividend.

Write the total number of equal cake pieces as the denominator and the number eaten as the numerator. Eating 3 of 8 equal pieces represents 3/8 of the cake.

Count all equal cells and the marked cells. Divide the whole amount by the denominator to find one equal part. Multiply that amount by the numerator. One cell does not necessarily represent one unit.

Divide the whole amount by the denominator to find one equal part. Multiply that amount by the numerator. A unit fraction has numerator 1, so division alone gives the answer.

Count the places where two line segments meet and the line changes direction. Every vertex of a closed polygon forms an angle, including inward corners. Endpoints of an open line do not form angles, and an ellipse has no corners.

Subtract each earlier term from the following term. A positive difference means adding that amount; a negative difference means subtracting its magnitude. Check the same operation against every neighbouring pair.

The given amount contains several equal parts. Divide it by the numerator to find one part, then multiply by the denominator to recover the whole. Check by finding the stated fraction of your whole.