Fractions: 4th grade math course download pdf.

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1 I. Addition and subtraction of two relative numbers in fractional writing :
2 II. Product of several numbers in fractional writing :
3 III. Quotient of two numbers with fractions

This math course on fractions covers addition, subtraction, multiplication and division of two fractions. The student will need to know the definition and be able to represent it on a graduated line in order to compare these fractions. Then, he will be able to develop skills in knowing how to perform the four operations on fractions and reduce them to the same denominator.

We will end this lesson with problem solving in eighth grade.

I. Addition and subtraction of two relative numbers in fractional writing :

Ownership:

Let a, b, c and d be four relative numbers such that $b\neq\,0\;d\neq0$ .

$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$ likewise, $\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}$

Example:

Calculate $A=-\frac{7}{9}+\frac{5}{6}$

We are looking for a common multiple of the denominators 9 and 6.

The first non-zero multiples of 9 are: 9, 18, 27 …

The first non-zero multiples of 6 are: 6, 12, 18, 24 …

We see that 18 is a common multiple of 9 and 6.

We are looking for the number equal to and the number equal to that have for

denominator 18 :

$A=-\frac{7}{9}+\frac{5}{6}\\A=-\frac{7\times \,6}{9\times \,6}+\frac{5\times \,9}{6\times \,9}\\A=-\frac{42}{54}+\frac{45}{54}\\A=\frac{-42+45}{54}\\A=\frac{3}{54}$

II. Product of several numbers in fractional writing :

Ownership:

Let a, b, c and d be four relative numbers such that $b\neq\,0\;d\neq0$ .

$\frac{a}{b}\times \,\frac{c}{d}=\frac{a\,\times \,c}{b\times \,d}$

Example:

Calculate $B=\frac{-14}{9}\times \,\frac{6}{-5}\times \,\frac{-3}{7}$ .

First, the sign of the result is determined by using the signs.

Here, all three factors are negative, so the product is negative.

The numerators are multiplied together and the denominators are multiplied together
Finally, we simplify the result:

$B=\frac{-14}{9}\times \,\frac{6}{-5}\times \,\frac{-3}{7}\\B=\frac{(-14)\times \,6\times \,(-3)}{9\times \,(-5)\times \,7}\\B=\frac{252}{-315}\\B=-\frac{252:63}{315:63}\\B=-\frac{4}{5}$

III. Quotient of two numbers with fractions

Ownership:

Dividing by a non-zero number means multiplying by its inverse.

Ownership:

Let a, b, c and d be four relative numbers such that $b\neq\,0\;d\neq0$ .

$\frac{a}{b}\,: \,\frac{c}{d}=\frac{a\,}{b\,}\times \frac{d}{c}$

Example:

Calculate $C=\frac{\frac{-4}{5}}{\frac{2}{15}}$

The inverse of the denominator is determined by “swapping” the

numerator and denominator.

Here the inverse of is $\frac{15}{2}$ .

The last fraction obtained is multiplied with the fraction that is at

numerator:

$C=\frac{\frac{-4}{5}}{\frac{2}{15}}\\C=\frac{-4}{5}\times \,\frac{15}{2}\\C=\frac{-4\times \,15\,}{5\times \,2}\\C=-\frac{2\times \,2\times \,5\times \,3}{5\times \,2}\\C=-\frac{2\times ,3}{1}\\C=6$

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Fractions: 4th grade math course PDF download.

I. Addition and subtraction of two relative numbers in fractional writing :

II. Product of several numbers in fractional writing :

III. Quotient of two numbers with fractions

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