Fractions Overview and Operations

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Questions and Answers

What is the total number of hectares allocated for the crops?

12 hectares

6 hectares

9 hectares (correct)

3 hectares

How is the total land divided based on the ratio of 2:3?

Into 5 parts (correct)

Into 10 parts

Into 7 parts

Into 4 parts

If the man wanted to change the ratio to 1:4, what would the total number of parts be?

6 parts (correct)

10 parts

5 parts

7 parts

What fraction of the land is allocated for sheltering animals?

2/5 Signup and view all the answers

What is the size of the smaller area for the animals in hectares?

4 hectares Signup and view all the answers

What is the ratio of cups of sugar to cups of flour in simplest form?

1:3 Signup and view all the answers

How many total cups are in the mixture of flour and sugar?

8 cups Signup and view all the answers

What fraction of the mixture is made up of flour?

3/4 Signup and view all the answers

Which of the following represents a rate?

60 km to 1 hour Signup and view all the answers

What is the lowest term of the ratio of flour to the total mixture?

3:4 Signup and view all the answers

If the number of cups of sugar was doubled, what would the new ratio of sugar to flour be?

4:3 Signup and view all the answers

Which of the following statements about ratios is correct?

Ratios can compare quantities with different units. Signup and view all the answers

What is the correct way to express the cups of sugar in relation to the cups of flour?

For every 6 cups of flour, 2 cups of sugar are used. Signup and view all the answers

What characterizes a proper fraction?

The numerator is less than the denominator. Signup and view all the answers

How can an improper fraction be defined?

The numerator is greater than the denominator. Signup and view all the answers

Which of the following is an example of a mixed number?

1 1/4 Signup and view all the answers

What is the first step to convert the improper fraction 5/4 into a mixed number?

Divide the numerator by the denominator. Signup and view all the answers

What describes the conversion of a mixed number to an improper fraction?

The numerator is multiplied by the denominator then added to the numerator. Signup and view all the answers

How would the improper fraction 9/4 be expressed as a mixed number?

1 3/4 Signup and view all the answers

Which statement about improper fractions and mixed numbers is true?

Improper fractions can be converted to mixed numbers. Signup and view all the answers

What is an example of an improper fraction?

4/3 Signup and view all the answers

How many pencils can be purchased with P36.75 if 2 pencils cost P10.50?

7 pencils Signup and view all the answers

How many workers are needed to tile the wall in 2 days if it takes 7 days for 6 workers?

21 workers Signup and view all the answers

How long will the corn last if there are 400 hens instead of 300?

15 days Signup and view all the answers

What is the total cost of 14 pencils if 2 pencils cost P10.50?

P73.50 Signup and view all the answers

If 300 hens can be fed for 20 days, how long would 150 hens last with the same amount of corn?

30 days Signup and view all the answers

In the wall tiling problem, how many total days would it take for 3 workers?

42 days Signup and view all the answers

If 6 workers can complete the job in 7 days, how many total days would it take for 2 workers?

42 days Signup and view all the answers

What is the direct proportional relationship established in the pencil purchase scenario?

Pencils to cost Signup and view all the answers

How do you add similar fractions?

Add the numerators and copy the denominator. Signup and view all the answers

What is the first step to add dissimilar fractions?

Find the least common denominator (LCD). Signup and view all the answers

When subtracting similar fractions, how is the operation performed?

Deduct the second numerator from the first and copy the denominator. Signup and view all the answers

What is the process for rewriting fractions when finding the LCD?

Divide the LCD by the original denominators. Signup and view all the answers

If you have the fractions 1/4 and 2/4, what is their sum?

3/4 Signup and view all the answers

Which of the following fractions simplifies correctly to 1?

4/4 Signup and view all the answers

If you subtract 6/8 from 7/8, what is the result?

1/4 Signup and view all the answers

For the fractions 1/2 and 1/3, what is the first step to add them?

Find the least common denominator. Signup and view all the answers

Study Notes

Fractions

Proper fractions have a numerator less than the denominator and represent a number less than 1
Improper fractions have a numerator greater than the denominator and represent a number greater than 1
Mixed numbers have a whole number and a fraction

Converting Fractions

To convert an improper fraction to a mixed number: divide the numerator by the denominator
To convert a mixed number to an improper fraction: multiply the denominator by the whole number, then add the numerator. The sum becomes the new numerator, the denominator stays the same

Adding and Subtracting Fractions

Similar fractions have the same denominator
To add similar fractions: add the numerators and copy the denominator
To subtract similar fractions: subtract the latter numerator from the first numerator, then copy the denominator
Dissimilar fractions have different denominators
To add or subtract dissimilar fractions: find the least common denominator (LCD), which is the smallest number divisible by both original denominators.
- Divide LCD by each original denominator and multiply the result with each original numerator.
- Add or subtract resulting fractions.

Ratios

Ratios compare quantities with the same unit.
Ratios can be expressed in colon form (e.g., 2:6) or fraction form (e.g., 2/6)
Ratio can be simplified

Rates

Rates compare quantities with different units
Rates are often expressed as a fraction (e.g., km/hr, ft/s, PhP/USD)

Direct Proportion

Direct proportion means as one quantity increase, the other increases proportionally.
If a:b = c:d then (a)(d) = (b)(c)

Indirect Proportion

Indirect proportion means as one quantity increases, the other decreases proportionally.
If a:b = c:d then (a)(c) = (b)(d)

Partitive Proportion

Dividing a number or quantity into parts based on a given ratio.
The sum of the parts in the ratio represents the total number of parts.
To find the value of each part, divide the total number by the total parts and multiply the result by the relevant part of the ratio.

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Description

This quiz covers the basics of fractions, including proper, improper, and mixed numbers. You will learn how to convert between these types, as well as how to add and subtract similar and dissimilar fractions using the least common denominator. Test your understanding of these fundamental concepts in this interactive quiz.