Full Grade 5 test

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.

For x − a = b, find the starting number by adding the difference and the amount subtracted: x = b + a. Substitute the result into the original equation and check by subtraction.

Equivalent fractions are made by multiplying or dividing both numerator and denominator by the same non-zero number. Changing only one, or adding the same number to both, does not preserve the value. Compare the denominators to find the divisor. Divide the numerator by that same number.

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

Subtract neighbouring terms to find the decrease at each step. Check that the decrease is constant throughout the sequence. Subtract this step from the last term.

Find the first multiple of the divisor strictly greater than the given number. Divide the number by the divisor, take the whole-number quotient, add 1 and multiply by the divisor. If the original number is already divisible, you still need the next multiple.

Work inside brackets first, then multiply and divide, and finally add and subtract. Perform operations of equal priority from left to right. Evaluate each option separately. The same numbers can give a different result when the brackets change.

Rewrite the fractions with a common denominator, scaling numerator and denominator by the same factor. Then subtract the numerators, not the denominators. Reduce the result by dividing numerator and denominator by a common factor.

The whole chart represents 100%. Find the specified category's share of the whole. If values are shown, divide the category value by the total and multiply by 100. If a sector is already labelled with a percentage, read its label.

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.

Equivalent fractions are made by multiplying or dividing both numerator and denominator by the same non-zero number. Changing only one, or adding the same number to both, does not preserve the value. Compare the denominators. Multiply the numerator by the same factor used for the denominator.

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.

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.

The total difference is the sum of equal interval values. Therefore, one interval equals the difference divided by the number of gaps. Equal gaps mean equal differences, not necessarily a difference of one.

The interval between consecutive whole numbers is divided into 10 equal parts, so each gap represents 0.1. Count the gaps from the left-hand number to A and add that many tenths.

A number is divisible by a divisor when division leaves no remainder. For 2, the last digit must be even; for 5, it must be 0 or 5; for 10, it must be 0. For 3 or 9, the sum of the digits must be divisible by 3 or 9 respectively. Check each option using the rule for the specified divisor.

A zero inside the number does not change the place values of other digits. Keep digits aligned by place value, calculate both partial products and add them.

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.

Undo the operations in reverse order. For a × x + b = c, first subtract b from c, then divide the difference by a: x = (c − b) ÷ a. Substitute the solution into the original equation to check.