Arithmetic Expressions: questions with answers

25 x 5 has the same factors as 5 x 25, so both have value 125. In a mixed expression, multiply before adding.

60 ÷ 2 uses division and has value 30. Different expressions can share a value. Multiplication and division take priority over addition and subtraction.

The values are 48, 47, 60, 55 and 40, so the order is 120 ÷ 3, 67 - 20, 67 - 19, 5 x 11, 35 + 25. Ordering by the first number written gives 5 x 11, 35 + 25, 67 - 19, 67 - 20, 120 ÷ 3, and pushing every multiplication to the end gives 120 ÷ 3, 67 - 20, 67 - 19, 35 + 25, 5 x 11; neither matches the values.

25 x 3 is worth 75 and 100 - 30 is worth 70, so 25 x 3 is greater. The largest number on the page, 100, sits in the expression with the SMALLER value: what is compared is the value, not the numbers written.

The first number rises by 1, and in a difference the amount taken away must move the SAME way by the same amount to cancel it, making the blank 78. That is the opposite of what balances a sum.

The first part falls by 1, so the second must move the opposite way by the same amount, making the blank 126. Leaving it as 125 would change the total, and moving it the same way as the first part changes it twice over.

It has 2, because only '+' separates terms and 6 x 3 counts as one. Counting the numbers instead gives 3.

The terms of 23 - 2 x 4 + 16 are 23, -2 x 4 and 16. A term is a part between '+' signs, so -2 x 4 stays whole even though it holds an operation.

The terms are 9 and 4 x 6. Working the second one out first gives 24, so the value is 33. Adding 9 into the term and then multiplying gives 78, the value of (9 + 4) x 6 instead.

She added 9 into the term 4 x 6 before working that term out. Each term is evaluated on its own first, so 4 x 6 is 24 and the value is 33, not 78.

Evaluate the bracketed addition first. Its whole value is subtracted, giving 20. Removing these brackets changes the value.

The bracket is worked out first: 15 + 56 is 71, and then 100 - 71, giving 29. Sweeping through from the left instead gives 141, which is what happens when the bracket is ignored.

A plus in front of a bracket leaves the terms inside just as they are. So 14 + (12 - 10) becomes 14 + 12 - 10. 14 + (-12 + 10) would become 14 - 12 + 10 instead.

50 - (15 - 6): the bracket collects 15 and -6, and the minus in front of it changes their signs back to what 50 - 15 + 6 has. 50 - (15 + 6) would need the signs inside to survive the bracket unchanged, and 50 + (-15 - 6) changes a sign that the plus in front leaves alone.

23 x 17 - 9 is larger. The bracketed form takes away 23 x 9. The other form takes away only 9. Taking away more leaves less, so the two forms are not equal. The difference inside the bracket stays a difference when the bracket is removed.