Photo AI

14 (a) Write each of the following ratios in their simplest form - OCR - GCSE Maths - Question 14 - 2019 - Paper 1

Question icon

Question 14

14-(a)-Write-each-of-the-following-ratios-in-their-simplest-form-OCR-GCSE Maths-Question 14-2019-Paper 1.png

14 (a) Write each of the following ratios in their simplest form. (i) 8 : 10 (ii) 300 ml : 2.1 litres (b) The ratio sin 30° : tan 45° can be written in the form 1... show full transcript

Worked Solution & Example Answer:14 (a) Write each of the following ratios in their simplest form - OCR - GCSE Maths - Question 14 - 2019 - Paper 1

Step 1

(i) 8 : 10

96%

114 rated

Answer

To simplify the ratio 8 : 10, we find the greatest common divisor (GCD) of 8 and 10, which is 2.

Dividing both terms by 2:

82:102=4:5\frac{8}{2} : \frac{10}{2} = 4 : 5

Thus, the simplified form is 4 : 5.

Step 2

(ii) 300 ml : 2.1 litres

99%

104 rated

Answer

First, convert 2.1 litres to millilitres:

2.1 litres=2.1×1000=2100 ml2.1 \text{ litres} = 2.1 \times 1000 = 2100 \text{ ml}

Now we have the ratio 300 ml : 2100 ml. To simplify, we find the GCD of 300 and 2100, which is 300.

Dividing both terms by 300:

300300:2100300=1:7\frac{300}{300} : \frac{2100}{300} = 1 : 7

Thus, the simplified form is 1 : 7.

Step 3

Find the value of n

96%

101 rated

Answer

To find the value of n in the ratio sin 30° : tan 45°, we first calculate each trigonometric function:

  • sin⁡30°=12\sin 30° = \frac{1}{2}
  • tan⁡45°=1\tan 45° = 1

The ratio is:

sin⁡30°tan⁡45°=121=12\frac{\sin 30°}{\tan 45°} = \frac{\frac{1}{2}}{1} = \frac{1}{2}

This can be written in the form 1 : n:

1:n=1:21 : n = 1 : 2

Therefore, n = 2.

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

Other GCSE Maths topics to explore

Number Toolkit

Maths - Edexcel

Prime Factors, HCF & LCM

Maths - Edexcel

Powers, Roots & Standard Form

Maths - Edexcel

Simple & Compound Interest, Growth & Decay

Maths - Edexcel

Fractions, Decimals & Percentages

Maths - Edexcel

Rounding, Estimation & Bounds

Maths - Edexcel

Surds

Maths - Edexcel

Algebraic Roots & Indices

Maths - Edexcel

Expanding Brackets

Maths - Edexcel

Factorising

Maths - Edexcel

Completing the Square

Maths - Edexcel

Algebraic Fractions

Maths - Edexcel

Rearranging Formulae

Maths - Edexcel

Algebraic Proof

Maths - Edexcel

Linear Equations

Maths - Edexcel

Solving Quadratic Equations

Maths - Edexcel

Simultaneous Equations

Maths - Edexcel

Iteration

Maths - Edexcel

Forming & Solving Equations

Maths - Edexcel

Functions

Maths - Edexcel

Coordinate Geometry

Maths - Edexcel

Estimating Gradients & Areas under Graphs

Maths - Edexcel

Real-Life Graphs

Maths - Edexcel

Transformations of Graphs

Maths - Edexcel

Sequences

Maths - Edexcel

Direct & Inverse Proportion

Maths - Edexcel

Standard & Compound Units

Maths - Edexcel

Exchange Rates & Best Buys

Maths - Edexcel

Geometry Toolkit

Maths - Edexcel

Angles in Polygons & Parallel Lines

Maths - Edexcel

Bearings, Scale Drawing, Constructions & Loci

Maths - Edexcel

Area & Perimeter

Maths - Edexcel

Right-Angled Triangles - Pythagoras & Trigonometry

Maths - Edexcel

Sine, Cosine Rule & Area of Triangles

Maths - Edexcel

Vectors

Maths - Edexcel

Transformations

Maths - Edexcel

Scatter Graphs & Correlation

Maths - Edexcel

Statistics

Maths - Edexcel

Ratio Analysis and Problem Solving

Maths - Edexcel

Inequalities

Maths - Edexcel

Volume, Area & Surface Area

Maths - Edexcel

The Circle

Maths - Edexcel

Probability

Maths - Edexcel

Trigonometry

Maths - Edexcel

Growth & Decay

Maths - Edexcel

Outliers

Maths - Edexcel

;