SBAC Math Grade 3 Operations and Fractions 2 — Questions and Answers

Question 1: What is 7 × 8?

54
56 (Correct answer)
63
64

Correct answer: 56

7 × 8 = 56. You can think of it as 7 groups of 8, or count by 8s: 8, 16, 24, 32, 40, 48, 56.

Multiplication represents groups of equal size. When we say 7 × 8, we mean 7 groups of 8 objects. You can find the answer by adding 8 seven times: 8 + 8 + 8 + 8 + 8 + 8 + 8 = 56. Another way to think about it: 7 × 8 is the same as (5 × 8) + (2 × 8) = 40 + 16 = 56. Using facts you know well to figure out harder facts is called the distributive property. A memory trick: 5, 6, 7, 8 — 56 = 7 × 8. The sequence 5, 6, 7, 8 helps you remember that 7 × 8 = 56. Knowing multiplication facts like 7 × 8 = 56 by heart helps you solve more complex math problems quickly. When you memorize facts, you free up mental energy for the harder parts of a problem.

Question 2: Which fraction is equivalent to 1/2?

2/6
3/6 (Correct answer)
2/3
3/4

Correct answer: 3/6

3/6 is equivalent to 1/2 because both the numerator and denominator of 1/2 are multiplied by 3: 1×3=3 and 2×3=6.

Equivalent fractions are different fractions that name the same amount. If you divide a candy bar into 2 equal pieces and take 1, you have 1/2. If you divide the same candy bar into 6 equal pieces and take 3, you still have the same amount — 3/6. To find equivalent fractions, multiply or divide both the numerator (top number) and denominator (bottom number) by the same nonzero number. For 1/2: multiply both by 2 to get 2/4; multiply both by 3 to get 3/6; multiply both by 4 to get 4/8. All of these equal 1/2. You can also check if fractions are equivalent by cross-multiplying: for 1/2 and 3/6, multiply 1 × 6 = 6 and 2 × 3 = 6. Since both products are equal, the fractions are equivalent. Understanding equivalent fractions is a building block for adding and subtracting fractions with different denominators, which you will learn in later grades. It is also important for comparing fractions — to compare 3/8 and 1/2, you can convert 1/2 to 4/8 and easily see that 4/8 > 3/8.

Question 3: There are 24 apples to be shared equally among 4 baskets. How many apples go in each basket?

4
5
6 (Correct answer)
8

Correct answer: 6

24 ÷ 4 = 6. When 24 items are divided equally into 4 groups, each group gets 6 items.

Division is the opposite of multiplication — it breaks a total into equal groups. The problem asks: how many apples go in each of the 4 baskets when 24 apples are shared equally? We solve this with 24 ÷ 4 = 6. We can check this by multiplying: 4 × 6 = 24. Multiplication and division are inverse operations — they undo each other. Knowing multiplication facts helps with division: since 4 × 6 = 24, we know 24 ÷ 4 = 6 and 24 ÷ 6 = 4. Another way to think about it: start with 24 apples and put them one at a time into baskets, going around until all are placed. You would put 6 in each basket. Word problems like this one require you to figure out which operation to use. Clue words that often signal division: 'shared equally,' 'divided by,' 'split into groups,' 'how many each.' Learning to recognize these helps you translate real-world situations into math.

Question 4: What is 9 × 0?

9
0 (Correct answer)
1
90

Correct answer: 0

Any number multiplied by 0 equals 0. This is the Zero Property of Multiplication: 9 × 0 = 0.

The Zero Property of Multiplication states that any number multiplied by zero is zero. This makes sense if you think about it concretely: if you have 9 bags with 0 apples each, you have 0 apples total. No matter how many groups you have, if each group has zero items, the total is zero. This is different from the Identity Property of Multiplication, which says that any number multiplied by 1 equals itself (9 × 1 = 9). The number 0 is special in multiplication — it 'erases' any other number and gives zero as the result. The Zero Property also works in the other order: 0 × 9 = 0. Multiplication is commutative, meaning you can switch the order and get the same answer. So 0 × 9 = 9 × 0 = 0. Understanding properties of multiplication — Zero Property, Identity Property, Commutative Property (3 × 4 = 4 × 3), and others — helps you understand how numbers behave and makes mental math easier.

Question 5: Which shows the fraction 3/4 correctly?

3 wholes divided by 4 groups
3 parts out of 4 equal parts of a whole (Correct answer)
4 parts out of 3 equal parts of a whole
3 groups of 4 items

Correct answer: 3 parts out of 4 equal parts of a whole

A fraction like 3/4 means the whole is divided into 4 equal parts, and we are considering 3 of those parts.

A fraction has two parts: the numerator (top number) and the denominator (bottom number). The denominator tells you how many equal parts the whole is divided into. The numerator tells you how many of those equal parts you are counting. For 3/4: the denominator is 4, which means the whole is divided into 4 equal pieces. The numerator is 3, which means we are counting 3 of those 4 pieces. Imagine a pizza cut into 4 equal slices — 3/4 means you have 3 of those slices. Fractions require equal parts. If a pizza is cut into 4 pieces but they are not equal, you cannot use 3/4 to describe 3 of them. The 'equal' part is essential to what makes a fraction work. Fractions can represent numbers less than one (like 3/4), equal to one (like 4/4 = 1 whole), or greater than one (like 5/4, which is more than one whole). Learning to visualize fractions using pictures — circles, rectangles, number lines — helps build a strong understanding of this important concept.

Question 6: Tamara solved 4 + 6 = 10 and then said that means 6 + 4 = 10 too. What property is she using?

Associative Property
Commutative Property (Correct answer)
Distributive Property
Zero Property

Correct answer: Commutative Property

The Commutative Property of Addition states that the order of addends can be switched without changing the sum: 4 + 6 = 6 + 4 = 10.

The Commutative Property of Addition states that you can add numbers in any order and the sum stays the same. In mathematical notation: a + b = b + a. Tamara is correctly applying this property: since 4 + 6 = 10, she knows 6 + 4 = 10 without having to calculate it again. The word 'commutative' comes from the Latin word for 'exchange' or 'swap.' You are swapping the order of the numbers. This works for addition (3 + 5 = 5 + 3 = 8) and multiplication (3 × 5 = 5 × 3 = 15), but NOT for subtraction (5 − 3 ≠ 3 − 5) or division (8 ÷ 4 ≠ 4 ÷ 8). The Associative Property is different — it says you can change the grouping of numbers: (2 + 3) + 4 = 2 + (3 + 4). The Distributive Property says you can distribute multiplication over addition: 3 × (4 + 2) = (3 × 4) + (3 × 2). Understanding these properties helps with mental math. If you know 4 + 6 = 10, you immediately know 6 + 4 = 10 too, saving time and effort. Properties are like rules that always work — knowing them makes math more efficient.

SBAC Math Grade 3 Operations and Fractions 2

What is 7 × 8?