Math  /  Numbers & Operations

QuestionThe tape diagrams below represent fraction multiplication. 1/51 / 5 skink
Which expression represents the image? Choose 1 answer: (A) 56×32\frac{5}{6} \times \frac{3}{2} (B) 14×34\frac{1}{4} \times \frac{3}{4} (c) 56×34\frac{5}{6} \times \frac{3}{4}

Studdy Solution

STEP 1

What is this asking? We need to figure out which multiplication problem matches the picture of the fraction diagrams. Watch out! Don't mix up the shaded parts with the total parts!

STEP 2

1. Analyze the first diagram.
2. Analyze the second diagram.
3. Combine the analysis.
4. Match to the answer.

STEP 3

Alright, let's break down this first diagram!
We see it's split in **two** equal parts.

STEP 4

Each part is labeled 12\frac{1}{2}, and that makes total sense because one out of two total parts *is* one-half!

STEP 5

We only have **one** of the two parts shaded, so this represents the fraction 12\frac{1}{2}.

STEP 6

Now, let's check out the second diagram!
This one's split into **four** equal parts.

STEP 7

Each part is labeled 14\frac{1}{4}, which is perfect, because one out of four total parts *is* one-fourth!

STEP 8

We've got **three** out of the four parts shaded in, so this represents the fraction 34\frac{3}{4}.

STEP 9

Okay, so the first diagram shows 12\frac{1}{2} and the second shows 34\frac{3}{4}.

STEP 10

The problem is asking about multiplying the fractions, and the picture shows one fraction *of* another.
That means we need to multiply!
So, we have 1234\frac{1}{2} \cdot \frac{3}{4}.

STEP 11

Let's look at the possible answers.
Answer (A) is 56×32\frac{5}{6} \times \frac{3}{2}.
Nope, that's not what we got!

STEP 12

Answer (B) is 14×34\frac{1}{4} \times \frac{3}{4}.
Hmm, close, but not quite right.

STEP 13

Answer (C) is 56×34\frac{5}{6} \times \frac{3}{4}.
Still not it!

STEP 14

Wait a second!
None of the answers match 1234\frac{1}{2} \cdot \frac{3}{4} exactly.
But the first diagram *is* 12\frac{1}{2}, and we can see that two of the four sections in the second diagram make up half of it.
So, another way to write 12\frac{1}{2} is 24\frac{2}{4}.

STEP 15

Now, let's rewrite our multiplication: 2434\frac{2}{4} \cdot \frac{3}{4}.
Since we're multiplying, we can simplify this to 1234\frac{1}{2} \cdot \frac{3}{4}.
Still no exact match!

STEP 16

Let's calculate 1234\frac{1}{2} \cdot \frac{3}{4}.
When we multiply fractions, we multiply the numerators (top numbers) together and the denominators (bottom numbers) together.
So, 13=31 \cdot 3 = 3 for the numerator, and 24=82 \cdot 4 = 8 for the denominator.
This gives us 38\frac{3}{8}.

STEP 17

Now, let's look at the diagram again.
We have 3 out of 8 sections shaded.
That's 38\frac{3}{8}!

STEP 18

Let's try answer (B) 14×34=1344=316\frac{1}{4} \times \frac{3}{4} = \frac{1 \cdot 3}{4 \cdot 4} = \frac{3}{16}.
This is not 38\frac{3}{8}.

STEP 19

Let's try answer (C) 56×34=5364=1524\frac{5}{6} \times \frac{3}{4} = \frac{5 \cdot 3}{6 \cdot 4} = \frac{15}{24}.
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 3.
So, 1524=15÷324÷3=58\frac{15}{24} = \frac{15 \div 3}{24 \div 3} = \frac{5}{8}.
This is not 38\frac{3}{8}.

STEP 20

The question asks for an expression that represents the image.
The image shows 12\frac{1}{2} of 34\frac{3}{4}.
This means 1234=38\frac{1}{2} \cdot \frac{3}{4} = \frac{3}{8}.
The second diagram is divided into fourths, and we have three of them shaded, which is 34\frac{3}{4}.
The first diagram is divided into halves, and we have one of them shaded, which is 12\frac{1}{2}.
We want 12\frac{1}{2} of the second diagram, which is 1234\frac{1}{2} \cdot \frac{3}{4}.
None of the answers match exactly, but we can rewrite 12\frac{1}{2} as 24\frac{2}{4}.
So, 2434=616\frac{2}{4} \cdot \frac{3}{4} = \frac{6}{16}.
Simplifying by dividing by 2 gives us 38\frac{3}{8}.
None of the answers match.
There might be a typo in the problem.

STEP 21

The correct expression representing the image is 12×34\frac{1}{2} \times \frac{3}{4}, which simplifies to 38\frac{3}{8}.
None of the provided answers match this.

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