QuestionCalculate $\frac{|3-1|+1}{10+2 \cdot 3}$ .

Studdy Solution

STEP 1

Assumptions1. The problem is a mathematical expression that needs to be simplified. . The order of operations to be followed is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This is often abbreviated as PEMAS.

STEP 2

First, we need to simplify the absolute value expression in the numerator. The absolute value of a number is its distance from zero on the number line, which is always positive or zero.
$|-1| = |2| =2$

STEP 3

Now, replace the absolute value expression in the numerator with the calculated value.
$\frac{2+1}{10+2 \cdot3}$

STEP 4

Next, simplify the addition in the numerator.
$\frac{2+1}{10+2 \cdot3} = \frac{3}{10+2 \cdot3}$

STEP 5

Now, simplify the multiplication in the denominator. According to the order of operations, multiplication should be done before addition.
$\frac{3}{10+2 \cdot3} = \frac{3}{10+}$

STEP 6

Next, simplify the addition in the denominator.
$\frac{3}{10+6} = \frac{3}{16}$

STEP 7

The expression is now fully simplified. The solution is $\frac{3}{16}$

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QuestionCalculate $\frac{|3-1|+1}{10+2 \cdot 3}$ .

Studdy Solution

STEP 1

Assumptions1. The problem is a mathematical expression that needs to be simplified. . The order of operations to be followed is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This is often abbreviated as PEMAS.

STEP 2

First, we need to simplify the absolute value expression in the numerator. The absolute value of a number is its distance from zero on the number line, which is always positive or zero.
$|-1| = |2| =2$

STEP 3

Now, replace the absolute value expression in the numerator with the calculated value.
$\frac{2+1}{10+2 \cdot3}$

STEP 4

Next, simplify the addition in the numerator.
$\frac{2+1}{10+2 \cdot3} = \frac{3}{10+2 \cdot3}$

STEP 5

Now, simplify the multiplication in the denominator. According to the order of operations, multiplication should be done before addition.
$\frac{3}{10+2 \cdot3} = \frac{3}{10+}$

STEP 6

Next, simplify the addition in the denominator.
$\frac{3}{10+6} = \frac{3}{16}$

STEP 7

The expression is now fully simplified. The solution is $\frac{3}{16}$

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QuestionCalculate ∣3−1∣+110+2⋅3\frac{|3-1|+1}{10+2 \cdot 3}10+2⋅3∣3−1∣+1​.

Studdy Solution

STEP 1

Assumptions1. The problem is a mathematical expression that needs to be simplified. . The order of operations to be followed is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This is often abbreviated as PEMAS.

STEP 2

First, we need to simplify the absolute value expression in the numerator. The absolute value of a number is its distance from zero on the number line, which is always positive or zero.∣−1∣=∣2∣=2|-1| = |2| =2∣−1∣=∣2∣=2

STEP 3

Now, replace the absolute value expression in the numerator with the calculated value.2+110+2⋅3\frac{2+1}{10+2 \cdot3}10+2⋅32+1​

STEP 4

Next, simplify the addition in the numerator.2+110+2⋅3=310+2⋅3\frac{2+1}{10+2 \cdot3} = \frac{3}{10+2 \cdot3}10+2⋅32+1​=10+2⋅33​

STEP 5

Now, simplify the multiplication in the denominator. According to the order of operations, multiplication should be done before addition.310+2⋅3=310+\frac{3}{10+2 \cdot3} = \frac{3}{10+}10+2⋅33​=10+3​

STEP 6

Next, simplify the addition in the denominator.310+6=316\frac{3}{10+6} = \frac{3}{16}10+63​=163​

STEP 7

The expression is now fully simplified. The solution is316\frac{3}{16}163​

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QuestionCalculate $\frac{|3-1|+1}{10+2 \cdot 3}$ .

First, we need to simplify the absolute value expression in the numerator. The absolute value of a number is its distance from zero on the number line, which is always positive or zero.
$|-1| = |2| =2$

Now, replace the absolute value expression in the numerator with the calculated value.
$\frac{2+1}{10+2 \cdot3}$

Next, simplify the addition in the numerator.
$\frac{2+1}{10+2 \cdot3} = \frac{3}{10+2 \cdot3}$

Now, simplify the multiplication in the denominator. According to the order of operations, multiplication should be done before addition.
$\frac{3}{10+2 \cdot3} = \frac{3}{10+}$

Next, simplify the addition in the denominator.
$\frac{3}{10+6} = \frac{3}{16}$

The expression is now fully simplified. The solution is $\frac{3}{16}$