Math / Numbers & Operations

QuestionDetermine whether the two pairs of numbers are proportional. 6,7 and 60,70
Are the number pairs proportional? No Yes

Studdy Solution

STEP 1

What is this asking? Do the ratios $6$ to $7$ and $60$ to $70$ represent the same relationship? Watch out! Don't just compare the numbers themselves; look at the relationship between them!

STEP 2

1. Simplify the ratios
2. Compare the simplified ratios

STEP 3

We have the ratio $6$ to $7$ , which can be written as the fraction $\frac{6}{7}$ .
Since $6$ and $7$ share no common factors other than $1$ , this fraction is already in its simplest form.
It's like a delicious single-scoop ice cream cone – perfect as it is!

STEP 4

Now, let's look at $60$ to $70$ .
We can write this as $\frac{60}{70}$ .
Both $60$ and $70$ are divisible by $10$ .
Dividing both the numerator and the denominator by $10$ gives us $\frac{60 \div 10}{70 \div 10} = \frac{6}{7}$ .
We've streamlined this fraction like a super-fast racing car!

STEP 5

We found that the simplified form of both ratios is $\frac{6}{7}$ .
Since both ratios simplify to the same fraction, they represent the same relationship.
It's like having two identical pizzas, even if one was initially cut into more slices!

STEP 6

Yes, the number pairs $6, 7$ and $60, 70$ are proportional.

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QuestionDetermine whether the two pairs of numbers are proportional. 6,7 and 60,70
Are the number pairs proportional? No Yes

Studdy Solution

STEP 1

What is this asking? Do the ratios $6$ to $7$ and $60$ to $70$ represent the same relationship? Watch out! Don't just compare the numbers themselves; look at the relationship between them!

STEP 2

1. Simplify the ratios
2. Compare the simplified ratios

STEP 3

We have the ratio $6$ to $7$ , which can be written as the fraction $\frac{6}{7}$ .
Since $6$ and $7$ share no common factors other than $1$ , this fraction is already in its simplest form.
It's like a delicious single-scoop ice cream cone – perfect as it is!

STEP 4

Now, let's look at $60$ to $70$ .
We can write this as $\frac{60}{70}$ .
Both $60$ and $70$ are divisible by $10$ .
Dividing both the numerator and the denominator by $10$ gives us $\frac{60 \div 10}{70 \div 10} = \frac{6}{7}$ .
We've streamlined this fraction like a super-fast racing car!

STEP 5

We found that the simplified form of both ratios is $\frac{6}{7}$ .
Since both ratios simplify to the same fraction, they represent the same relationship.
It's like having two identical pizzas, even if one was initially cut into more slices!

STEP 6

Yes, the number pairs $6, 7$ and $60, 70$ are proportional.

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QuestionDetermine whether the two pairs of numbers are proportional. 6,7 and 60,70Are the number pairs proportional? No Yes

Studdy Solution

STEP 1

What is this asking? Do the ratios 666 to 777 and 606060 to 707070 represent the same relationship? Watch out! Don't just compare the numbers themselves; look at the *relationship* between them!

STEP 2

1. Simplify the ratios2. Compare the simplified ratios

STEP 3

We have the ratio 666 to 777, which can be written as the fraction 67\frac{6}{7}76​.Since 666 and 777 share no common factors other than 111, this fraction is already in its simplest form.It's like a delicious single-scoop ice cream cone – perfect as it is!

STEP 4

STEP 5

We found that the simplified form of both ratios is 67\frac{6}{7}76​.Since both ratios simplify to the same fraction, they represent the same relationship.It's like having two identical pizzas, even if one was initially cut into more slices!

STEP 6

Yes, the number pairs 6,76, 76,7 and 60,7060, 7060,70 are proportional.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionDetermine whether the two pairs of numbers are proportional. 6,7 and 60,70
Are the number pairs proportional? No Yes

What is this asking? Do the ratios $6$ to $7$ and $60$ to $70$ represent the same relationship? Watch out! Don't just compare the numbers themselves; look at the relationship between them!

1. Simplify the ratios
2. Compare the simplified ratios

We have the ratio $6$ to $7$ , which can be written as the fraction $\frac{6}{7}$ .
Since $6$ and $7$ share no common factors other than $1$ , this fraction is already in its simplest form.
It's like a delicious single-scoop ice cream cone – perfect as it is!

We found that the simplified form of both ratios is $\frac{6}{7}$ .
Since both ratios simplify to the same fraction, they represent the same relationship.
It's like having two identical pizzas, even if one was initially cut into more slices!

Yes, the number pairs $6, 7$ and $60, 70$ are proportional.